%!
% This file is a NONconforming PostScript file.
(TeXPS: dvi->PostScript Driver dvitps, Version 3.9 of July 23, 1990\n)print flush
% Copyright 1989 Stephan v. Bechtolsheim (unless otherwise stated)
% applies to various prologue files. Read documentation for details.
save
% dvitps: BEGIN including file "/usr/local/lib/tex/TeXPS/pro/texpre.pro"
/@bop0
{
PsPrintEnabled { (Pass0: Page ) print == flush } {pop} ifelse
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/@eop0 {
pop
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/@bop1
{
PsPrintEnabled { (Pass1: Page ) print == flush } {pop} ifelse
save
DviTranslateVector-X DviTranslateVector-Y translate
DviOrientationMatrix concat
Page-H-Offset Page-V-Offset translate
3 1 roll
translate
0 0 moveto
Draft-Flag { @Draft } if
/DriverDelta 0 def
} def
/@eop1 {
pop
showpage
restore
} def
/@end {
(Done!\n) print flush
} def
/@ReportVmStatus {
(\n@ReportVmStatus: ) print
print (: ) print
vmstatus
(max: ) print 20 string cvs print
(, used: ) print 20 string cvs print
(, level: ) print 20 string cvs print
(\n) print flush
} def
/@ReportVmStatusNew {
(VM: ) print
exch print
(, printer: ) print
/Vmfree vmstatus pop exch pop def Vmfree (       ) cvs print
(, driver: ) print dup (      ) cvs print
(, delta: ) print
Vmfree sub (      ) cvs print
(\n) print flush
} def
/@Draft {
gsave
Page-H-Offset neg Page-V-Offset neg translate
-45 rotate
-150 0 moveto
/Helvetica-Bold findfont
[120.0 0 0 -120.0 0 0 ] makefont setfont
(DRAFT) show
grestore
gsave
Page-H-Offset neg Page-V-Offset neg translate
300 -100 moveto
/Helvetica-Bold findfont
[60.0 0 0   -60.0 0 0 ] makefont setfont
Date-and-Time		show
(   ::   )	      	show
Dvi-File-Name		show
grestore
} def
/@snl {show currentpoint exch pop 72 exch moveto 0 -10 rmoveto}def
/DoError {
/Courier-Bold findfont 12 scalefont setfont
72 720 moveto
(dvitps ERROR: ) show Dvi-File-Name show ( @ ) show HostName show
/Courier findfont 10 scalefont setfont
72 700 moveto
{/charcode exch def /thechar ( ) dup 0 charcode put def
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{/charcode exch def /thechar ( ) dup 0 charcode put def
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showpage
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/FatalFontList (Certain fonts that you have requested in your dvi file could not be:\
found on the system. Either these fonts have not been installed or they:\
do not exist in the magnifications you have requested. If the fonts are:\
installed, they will be in the directory /usr/local/lib/fonts/gf. The:\
standard font magnifications at Rutgers are 0, 0.5, 1, 1.5, 2, 3, 4, 5,:\
6, 7, 8, and 9, corresponding to the numerical file extensions of fonts:\
in the above directory. If the filenames below differ only by numerical:\
extension to the ones in the directory, try adjusting your magnifications.:\
If the fontnames are not there at all, the font is not installed at Rutgers.:\
See the local TeX supporter.::\
The fonts which could not be found are listed below.::) def
/FontSubstitutionList (Certain fonts that you requested in your dvi file could not be found:\
on the system. In order to print your document, other fonts that are:\
installed were substituted for these missing fonts.::\
Below is a list of the substitutions that were made.::) def
/NoAvailableFonts (None of the fonts can be found on the above host. If you did not set:\
the TEXFONTS environment variable incorrectly, contact the operator or:\
the local system administrator.:) def
% dvitps: END including file "/usr/local/lib/tex/TeXPS/pro/texpre.pro"
% dvitps: BEGIN including file "/usr/local/lib/tex/TeXPS/pro/pos.pro"
/a { rmoveto } def
/DriverDelta 0 def
/b { exch p dup /DriverDelta exch def 0 rmoveto } def
/c { p DriverDelta 4 sub dup /DriverDelta exch def 0 rmoveto } def
/d { p DriverDelta 3 sub dup /DriverDelta exch def 0 rmoveto } def
/e { p DriverDelta 2 sub dup /DriverDelta exch def 0 rmoveto } def
/f { p DriverDelta 1 sub dup /DriverDelta exch def 0 rmoveto } def
/g { p DriverDelta 0 rmoveto } def
/h { p DriverDelta 1 add dup /DriverDelta exch def 0 rmoveto } def
/i { p DriverDelta 2 add dup /DriverDelta exch def 0 rmoveto } def
/j { p DriverDelta 3 add dup /DriverDelta exch def 0 rmoveto } def
/k { p DriverDelta 4 add dup /DriverDelta exch def 0 rmoveto } def
/l { p -4 0 rmoveto } def
/m { p -3 0 rmoveto } def
/n { p -2 0 rmoveto } def
/o { p -1 0 rmoveto } def
/q { p 1 0 rmoveto } def
/r { p 2 0 rmoveto } def
/s { p 3 0 rmoveto } def
/t { p 4 0 rmoveto } def
/p { show } def
/w { 0 exch rmoveto } def
/x { 0 rmoveto } def
/y { 3 -1 roll p rmoveto } def
/u-string ( ) def
/u { u-string exch 0 exch put
u-string show
} def
/v { u-string exch 0 exch put
currentpoint
u-string show
moveto
} def
% dvitps: END including file "/usr/local/lib/tex/TeXPS/pro/pos.pro"
% dvitps: BEGIN including file "/usr/local/lib/tex/TeXPS/pro/rules.pro"
/z
{   /dy exch def
/dx exch def
currentpoint
currentpoint
transform round exch round exch itransform
newpath
moveto
dx 0 rlineto
0 dy rlineto
dx neg 0 rlineto
closepath
fill
moveto
}
def
/z
{   /dy exch def
/dx exch def
currentpoint
0.2 0.2 rmoveto
currentpoint
newpath
moveto
dx 0 rlineto
0 dy rlineto
dx neg 0 rlineto
closepath
fill
moveto
}
def
% dvitps: END including file "/usr/local/lib/tex/TeXPS/pro/rules.pro"
/Dvi-File-Name (maros.dvi) def
(Dvi file name: ") print Dvi-File-Name print (".\n) print
/Draft-Flag false def
/#copies 1 def
/NumCharsInPixelFonts 256 def
/HostName (konig.rutgers.edu) def
(This PostScript file was produced on host \") print HostName print (\".\n) print
/PsPrintEnabled true def
/Page-H-Offset   0.000000 def
/Page-V-Offset   0.000000 def
/ExecPsConv {0.30 mul} def
/Date-and-Time (Thu Jan 28 16:27 1993) def
/DviTranslateVector-X   72.000 def
/DviTranslateVector-Y  720.000 def
/DviOrientationMatrix [    0.240    0.000    0.000
	   -0.240 0.0 0.0 ] def
% dvitps: BEGIN including file "/usr/local/lib/tex/TeXPS/pro/pixel-fonts.pro"
/@newfont
{
/newname exch def
newname 7 dict def
newname load begin
/FontType 3 def
/FontMatrix [1 0 0 -1 0 0] def
/FontBBox [0 0 1 1] def
/BitMaps NumCharsInPixelFonts array def
/BuildChar {CharBuilder} def
/Encoding NumCharsInPixelFonts array def
0 1 NumCharsInPixelFonts 1 sub {Encoding exch /.undef put} for
end
newname newname load definefont pop
} def
/ch-image {ch-data 0 get} def
/ch-width {ch-data 1 get} def
/ch-height {ch-data 2 get} def
/ch-xoff  {ch-data 3 get} def
/ch-yoff  {ch-data 4 get} def
/ch-tfmw  {ch-data 5 get} def
/CharBuilder
{
/ch-code exch def
/font-dict exch def
/ch-data font-dict /BitMaps get ch-code get def
ch-data null eq not
{
ch-tfmw   0
ch-xoff neg
ch-height ch-yoff sub neg
ch-width  ch-xoff neg add
ch-yoff
setcachedevice
0 0 transform round exch round exch itransform translate
ch-width ch-height true
[1 0  0 1 ch-xoff ch-height ch-yoff sub] {ch-image} imagemask
}
if
} def
/@dc
{
/ch-code exch def
/ch-data exch def
currentfont /BitMaps get
ch-code ch-data put
currentfont /Encoding get
ch-code (   ) cvs   % convert the character code to a string
cvn
ch-code exch put
} def
/@sf /setfont load def
% dvitps: END including file "/usr/local/lib/tex/TeXPS/pro/pixel-fonts.pro"

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	 19 14 0 13 20] 110 @dc
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	 19 14 0 13 20] 117 @dc
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	 13 23 0 22 11] 102 @dc
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	 9 23 0 22 10] 108 @dc
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	 18 14 -2 13 20] 110 @dc
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1 @eop0

0 0 1 @bop1 59 w @F16 @sf(DIMA)o(CS)10 b(Series)g(in)g(Discrete)f
(Mathematics)-546 25 y(and)h(Theoretical)f(Computer)g(Science)-463 26 y(V)n
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23 b(Ev)l(alua)q(tion)-1048 74 y(of)h(the)e(MINET)h(Minim)n(um)h(Cost)f
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(AN)14 b(MAR)o(OS)-738 122 y @F1 @sf(Abstra)o(ct.)20 b @F18 @sf(In)8 b
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13 x(net\015o)o(w)g(solv)o(er)o(.)23 b(The)14 b(e\013ect)f(of)h(t)o(w)o(o)g
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41 y(computer)c(are)h(also)g(analyz)o(ed)f(and)h(some)g(imp)q(ortan)o(t)o 
11 x(facts)f(are)h(rev)o(eale)o(d.)-625 187 y @F9 @sf(1.)24 b(In)o(tro)q
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54 y(lenge)j(for)g(researc)o(he)q(rs)i(in)e(the)g(\014eld.)25 b(The)16 b
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11 b(MINET)-1444 54 y(w)o(as)f(tested,)i(as)e(required)h(b)o(y)f([)p @F9 @sf
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54 y(metho)q(ds)d(to)f(\014nd)h(some)f(relationship)g(b)q(et)o(w)o(een)i
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15 b(discussion)h(is)f(presen)o(ted)i(in)d(section)i(3.)21 b(Next,)16 b(a)f
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@F18 @sf(1991)10 b @F3 @sf(Mathematics)k(Subje)n(ct)g(Classi\014c)n(ation)p 
@F18 @sf(.)j(90C35.)-756 41 y(This)11 b(researc)o(h)f(w)o(as)i(supp)q(or)o
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(und)h(OTKA)j(2587.)o -356 57 a @F16 @sf(c)-22 1 y @F10 @sf(\015)p @F16 @sf
(0000)d(American)f(Mathematical)f(So)q(ciet)o(y)-482 29 y(0000-00)q(00/00)q 
12 x($1.00)i(+)f($.25)h(p)q(er)f(page)-732 100 y @F18 @sf(1)-731 b
1 @eop1

2 @bop0
@F18 @sf
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	 23 23 -1 22 26] 86 @dc
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	 6 6 -7 22 18] 19 @dc
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000C00F0000C00F0000000F0000000F0000000F00000007800000078000000780000003C00
00003C0001801E0001801E0001800F000180070001C0038003C001E003C000F007C0007E0E
E0001FFC600003F020>
	 27 30 -6 28 30] 67 @dc
[<
C0006000300018000C00060003000300018001C000C000E000600070003000380038001800
1C001C000C000E000E000E0006000600060007000700070007000700060006000600060006
000C000C000800100010>
	 16 42 0 30 17] 41 @dc
@F9 @sf
[<
C3FC00EFFF00FC03C0F001C0E000E0C000E0C000F0C000F00000F00001F00003F0007FE007
FFE00FFFC03FFF803FFF007FFE00FFE000FE0000F80000F00060F00060F000E07000E07801
E03C07E01FFEE007F860>
	 20 28 -3 27 27] 83 @dc
[<
FFE000FFE0001F00001F00001F00001F00001F00001F00001F1F801F7FE01FC1F01F80F81F
00FC1F007C1F007E1F007E1F007E1F007E1F007E1F007E1F007C1F00FC1F00F81FC1F8FFFF
E0FF1FC0>
	 23 26 -1 17 27] 112 @dc
@F4 @sf
[<
FFF000FFF00007800007800007800007800003C00003C00003C00003C00001E00001E00001
E00001E00000F00000F00000F00000F000007800007800007800007800003C00003C00003C
00003C0001FFE001FFE0>
	 19 28 -2 27 16] 73 @dc
[<
C0E061F873FC3C1C18060C0606020300018000C0006000300018180C0C1C0FF607E301C3>
	 16 18 -2 17 17] 122 @dc
[<
E0F0F8F870>
	 5 5 -5 4 13] 46 @dc
@F20 @sf
[<
7FFFFFC0FFFFFFE00000000000000000000000000000000000000000000000000000000000
000000FFFFFFE07FFFFFC0>
	 27 12 -2 15 32] 61 @dc
@F15 @sf
[<
1801801E0038038033001C01C071801C01C070C01C01C038C01C01C038C00E00E038400E00
E01C000E00E01C000E00E01C000700700E000700700E00C780700E00C780780E0063407C0E
006320760E002718630C001C0FC0F800>
	 34 18 -1 17 36] 109 @dc
@F4 @sf
[<
FFF00000FFF000000780000007800000078000000780000003C0000003C0000003C0000003
C0000001E0000001E0000001E0000001FFF80000F01E0000F0070000F0038000F003C00078
01C0007801E0007801E0007801E0003C01E0003C01E0003C01E0003C03C001FFFF8001FFFE
00>
	 27 28 -2 27 28] 80 @dc
[<
7F0000E18000F0E000F0600060700000700000380000380007B8000CF800183C00383C0038
1C00381C003C0E003C0E003C0E003C0E001E07001E07000E07000F070007078003878001CF
80007980>
	 17 26 -2 17 19] 103 @dc
@F20 @sf
[<
00060000000600000006000000060000000600000006000000060000000600000006000000
060000000600000006000000060000FFFFFFE0FFFFFFE00006000000060000000600000006
00000006000000060000000600000006000000060000000600000006000000060000000600
00>
	 27 28 -2 23 32] 43 @dc
[<
FFF8FFF8070007000700070007000700070007000700070007000700070007000700070007
000700070007000700C700FF003F0007000300>
	 13 28 -4 27 21] 49 @dc
@F4 @sf
[<
03C006200C100C181C0C0C0C0E040E060E060E0607030703C3834387638F238F138F0F06>
	 16 18 -3 17 19] 118 @dc
@F9 @sf
[<
07F8001FFE00381F007C1F80FE0FC0FE0FE0FE0FE0FE0FE07C0FE0380FE0000FC0000FC000
1F80001E0003F80003FC00003E00001F003C1F807E1FC07E0FC07E0FC07E0FC03C1F801C1F
800FFE0003F800>
	 19 27 -2 26 24] 51 @dc
@F4 @sf
[<
07C000001FF0000038380000700C000070060000F0030000F0018000F0018000F000C000F0
00C000F000C000780060007800600078006000780060003C0030003C0030003C0030003C00
30001E0018001E0018001E0018001E0018000F000C000F000C000F000C000F000E007FF87F
E07FF87FE0>
	 27 29 -8 27 31] 85 @dc
[<
FF8000FF80001C00001C00001C00001C00000E00000E00000E78000E8C0007860007070007
03800703C00381C00381E00381E00381E001C0F001C0F031C0F031E0E018E0E018F0E00CD8
C0078780>
	 20 26 -1 17 21] 112 @dc
@F20 @sf
[<
001F0000007FC00000E0E00001C030000380300007801800070018000F000C000F000C000F
000C000F000C000F000C000F000C000F000C000F000C000F000C000F000C000F000C000F00
0C000F000C000F000C000F000C000F000C000F000C000F000C000F000C000F001E00FFF0FF
C0FFF0FFC0>
	 26 29 -2 27 31] 85 @dc
@F20 @sf
[<
402010080804040474FCFCF870>
	 6 13 -3 28 12] 39 @dc

3 @eop0

0 0 3 @bop1 353 -58 a @F18 @sf(PERF)o(ORMANC)q(E)16 b(EV)l(ALUA)q -3 x
(TION)q 17 x(OF)f(MINET)337 b(3)-1445 100 y @F20 @sf(-)14 b @F15 @sf(p)p 
@F20 @sf(\()p @F15 @sf(i)p @F20 @sf(\))43 b(predece)q(ssor)16 b(of)d(no)q
(de)h @F15 @sf(i)p @F20 @sf(,)-531 53 y(-)g @F15 @sf(s)p @F20 @sf(\()p 
@F15 @sf(i)p @F20 @sf(\))45 b(thread)14 b(succe)q(ssor)i(of)d(no)q(de)h 
@F15 @sf(i)p @F20 @sf(,)-621 54 y(-)g @F15 @sf(t)p @F20 @sf(\()p @F15 @sf
(i)p @F20 @sf(\))49 b(cardinalit)o(y)13 b(of)g(subtree)i(headed)g(b)o(y)f
(no)q(de)g @F15 @sf(i)p @F20 @sf(,)-863 54 y(-)g @F15 @sf(f)t @F20 @sf(\()p 
@F15 @sf(i)p @F20 @sf(\))40 b(last)13 b(no)q(de)i(in)e(subtree)q 15 x
(headed)i(b)o(y)e(no)q(de)h @F15 @sf(i)p @F20 @sf(,)-835 54 y(-)g @F15 @sf
(id)p @F20 @sf(\()p @F15 @sf(i)p @F20 @sf(\))28 b(directed)15 b(no)q(de)f
(iden)o(ti\014er)h(of)e(the)h @F15 @sf(i)p @F20 @sf(th)h(basic)f(arc.)-879 
70 y(MINET)j(is)g(equipp)q(ed)g(with)g(a)f(newly)h(designed)g(column)g
(selection)g(\(pricing\))g(tec)o(h-)-1444 54 y(nique,)c(called)f(NETPRI,)h
(describ)q(ed)h(in)e([)p @F9 @sf(9)p @F20 @sf(],)g(that)h(can)g(tak)o(e)g
(adv)n(an)o(tage)f(of)g(a)g(recognized)-1443 54 y(structure)q 19 x(of)18 b
(a)g(problem.)31 b(The)19 b(purp)q(ose)g(of)f(this)g(tec)o(hnique)h(is)g
(to)f(reduce)i(the)f(o)o(v)o(er-)-1445 54 y(all)14 b(computational)g
(e\013ort)j(sp)q(en)o(t)f(on)f(pricing.)23 b(It)15 b(is)h(con)o(trolled)f
(b)o(y)g(3)g(parameters.)24 b(By)-1444 54 y(sp)q(ecial)18 b(setting)g(of)f
(them,)h(it)f(is)h(p)q(ossible)f(to)h(repro)q(duce)h(most)f(of)f(the)h
(kno)o(wn)f(pricing)-1445 54 y(strategies.)-132 56 y(Due)f(to)g(the)h
(fact)f(that)g(randomly)f(generated)j(problems)e(usually)f(do)h(not)g(ha)o
(v)o(e)g(an)o(y)-1445 54 y(recognizable)c(structure,)h(this)e
(sophisticated)h(pricing)f(feature)h(of)e(MINET)i(w)o(as)f(not)g(used)-1444 
53 y(during)i(the)i(exp)q(erimen)o(ts.)k(The)14 b(presen)o(t)h(\014xed)f
(setting)g(of)f(the)i(parameters)f(repro)q(duce)q(s)-1443 54 y(the)g @F4 @sf
(le)n(ast)h(r)n(e)n(c)n(ently)f(c)n(onsider)n(e)n(d)h(\(LR)o(C\))f @F20 @sf
(en)o(tering)g(rule)g([)p @F9 @sf(2)p @F20 @sf(].)-903 56 y(The)h(most)g
(imp)q(ortan)o(t)f(parts)h(of)g(the)g(main)f(algorithmi)o(c)g(steps)j(of)d
(MINET,)h(as)g(used)-1444 54 y(during)f(the)g(testing,)g(can)g(b)q(e)g
(summarized)g(as)g(follo)o(ws.)-851 84 y @F9 @sf(Step)h(0.)20 b @F4 @sf
(Initialization.)f @F20 @sf(Create)d(all{l)o(ogi)o(cal)d(basis.)20 b(Set)
15 b(principal)e(pricing)h(p)q(oin)o(ter)-1295 54 y @F15 @sf(p)e @F20 @sf
(=)g @F15 @sf(m)i @F20 @sf(\(the)h(n)o(um)o(b)q(er)f(of)f(edges\))i(and)f
(set)h(up)f(pricing)f(v)o(ector.)-1105 55 y @F9 @sf(Step)g(1.)18 b @F4 @sf
(Pricing.)f @F20 @sf(Start)c(pricing)g(at)f @F15 @sf(p)7 b @F20 @sf(+)g(1)
13 b(\(mo)q(d)f @F15 @sf(m)p @F20 @sf(\),)h(price)g(the)h(non)o(basic)e
(arcs)i(and)-1296 54 y(stop)j(at)f(the)h(\014rst)g(impro)o(ving)d(arc.)26 b
(Set)16 b(p)q(oin)o(ter)h @F15 @sf(p)f @F20 @sf(to)g(the)h(index)f(of)f
(this)i(arc.)-1296 54 y(If)h(no)f(impro)o(ving)f(arc)i(can)g(b)q(e)h
(found,)f(stop)g(\(solution)f(optimal)o(,)g(or)h(problem)-1296 54 y
(infeasible\).)-295 56 y @F9 @sf(Step)h(2.)30 b @F4 @sf(Pivot.)g @F20 @sf
(T)m(race)18 b(the)g(lo)q(op)f(created)j(b)o(y)d(the)i(en)o(tering)f(arc)g
(in)f(the)i @F15 @sf(T)k @F20 @sf(basis)-1295 54 y(tree)18 b(and,)e(sim)o
(ultaneously)m(,)o 15 x(do)g(the)h(ratio)e(test.)25 b(Start)17 b(from)e(b)q
(oth)h(endp)q(oin)o(ts)-1295 54 y(of)g(this)h(arc)g(and)f(mo)o(v)o(e)g(up)o
(w)o(ards)g(in)g(the)h(direction)g(of)f(the)h(ro)q(ot)f(of)g @F15 @sf(T)
6 b @F20 @sf(.)26 b(Mo)o(v)o(e)-1296 54 y(alw)o(a)o(ys)15 b(on)g(the)h
(smaller)f(subtree.)24 b(Stop)16 b(ratio)f(test)h(immediately)e(if)h(a)g
(0)g(ratio)-1296 54 y(is)f(encoun)o(tere)q(d.)19 b(The)c(corresp)q(onding)f
(arc)h(will)d(lea)o(v)o(e)i(the)g(basis.)-1163 55 y @F9 @sf(Step)g(3.)19 b 
@F4 @sf(Up)n(dating.)f @F20 @sf(Up)q(date)d(solution,)d @F15 @sf(T)6 b 
@F20 @sf(,)14 b(and)g(pricing)f(v)o(ector.)19 b(Go)13 b(to)h(step)h(1.)-1328 
84 y(Step)f(2)f(ensures)q 15 x(that)g(the)i(\\smaller)d(subtree)q(")i
(will)e(alw)o(a)o(ys)h(b)q(e)h(as)g(small)e(as)i(p)q(ossible,)-1445 54 y
(th)o(us)g(up)q(dating)g(w)o(ork)f(will)g(b)q(e)h(reduced)q 15 x(to)g(a)f
(minim)o(um)o(.)-879 56 y(Logically)o 16 x(the)19 b(most)e(complicated)g
(part)h(of)f(the)h(program)f(is)h(the)g(up)q(dating)f(of)g(the)-1444 54 y
(basic)12 b(spanning)g(tree.)18 b(In)12 b(step)h(2,)e(there)j(is)d(an)h
(e\013ort)h(to)e(minimize)g(this)h(w)o(ork.)17 b(In{depth)-1444 54 y(in)o
(v)o(estigation)d(has)i(sho)o(wn)g(that,)g(after)g(all,)f(up)q(dating)g
(is)h(a)f(less)h(decisiv)o(e)h(factor)f(in)f(the)-1444 54 y(running)k
(time)g(of)g(MINET)g(than)g(pricing.)34 b(T)m(able)19 b(5)g(and)g(mo)q
(del)f(\(4.1\))h(in)g(section)h(4)-1445 54 y(sho)o(w)15 b(an)f(example)h
(that,)g(b)o(y)f(Sp)q(earman's)h(rank)g(correlation,)g(there)h(ma)o(y)e(b)q
(e)h(a)g(p)q(erfect)-1443 54 y(p)q(ositiv)o(e)c(relationship)g(b)q(et)o(w)o
(een)i(the)f(n)o(um)o(b)q(er)f(of)g(scanned)i(v)n(ariables)e(and)g
(solution)f(time.)-1445 54 y(The)16 b(same)g(is)f(usually)g(not)g(true)i
(for)e(the)h(relation)f(b)q(et)o(w)o(een)i(the)f(n)o(um)o(b)q(er)g(of)f
(iterations)-1445 54 y(\(whic)o(h,)e(in)f(most)g(cases,)i(is)f(a)f(go)q(o)q
(d)g(estimate)i(of)e(the)h(tree)h(up)q(dates\))g(and)e(solution)g(time.)
-1445 54 y(Simila)o(r)h(observ)n(ations)h(ha)o(v)o(e)g(b)q(een)h(made)e
(on)h(a)g(large)f(n)o(um)o(b)q(er)h(of)g(other)g(problems.)-1311 55 y
(MINET)20 b(has)g(b)q(een)h(used)g(to)e(solv)o(e)h(large)f(scale)i
(real{life)d(problems)i(for)g(a)f(couple)-1444 54 y(of)d(y)o(ears.)25 b
(During)15 b(this)h(p)q(erio)q(d)h(it)f(encoun)o(tered)i(a)e(large)f(n)o
(um)o(b)q(er)i(of)e(v)o(ery)i(degenerate)-1443 b
3 @eop1

4 @bop0
@F18 @sf
[<
03FE03FE0070007000700070FFFEFFFEC07060703070187008700C7006700370017001F000
F000700030>
	 15 21 -1 20 18] 52 @dc
@F20 @sf
[<
3E006180F1C0F0C060E000E000E000E000E000E000E000E000E000E000E000E000E000E000
E000E000E000E000E000E00FE00FE000000000000000000000000001C003E003E003E001C0
>
	 11 37 3 28 13] 106 @dc
@F4 @sf
[<
180600F0380E01981C07038C1C0703841C0701C61C0701C60E0381C20E0380E00E0380E00E
0380E00701C0700701C070C701C070C781E07063C1F0706341D07033318C601E1F07C0>
	 31 18 -3 17 34] 109 @dc
[<
03C7000E6C800C3CC00C1C601C1C601C1C600E0E200E0E000E0E000E0E00070700070700C3
87004387006383802383801383800F0180>
	 19 18 -3 17 22] 117 @dc
[<
780000EC0000F60000F7000067000007000003800003800003800003800003C00001C00001
C00001C00001C00000E00000E00000E00000E00000E00000700000700000700000700007FF
8003FF80003800003800003800003800003800001C00001CC0001DE0000CF00006600003C0
>
	 20 37 1 28 13] 102 @dc
@F20 @sf
[<
FFF3FFC0FFF3FFC00F003C000F003C000F003C000F003C000F003C000F003C000F003C000F
003C000F003C000F003C000F003C000F003C000FFFFC000FFFFC000F003C000F003C000F00
3C000F003C000F003C000F003C000F003C000F003C000F003C000F003C00FFF3FFC0FFF3FF
C0>
	 26 28 -2 27 31] 72 @dc
[<
C000C0006000600060003000300030001800180018000C000C000C00060006000300030003
0001800180018000C000C000C000600060003000300030001800180018000C000C000C0006
0006000600030001>
	 16 41 -2 30 21] 47 @dc
/@F12 @newfont
@F12 @sf
[<
003C00E001C001800380038003800380038003800380038003800380038003800380030007
001C00F0001C00070003000380038003800380038003800380038003800380038003800380
018001C000E0003C>
	 14 41 -3 30 21] 102 @dc
@F4 @sf
[<
7800EE00F700F3006380038001C001C001C001C000E000E000E000E0007000700070007000
3800380C38063806180218011800F0000000000000000000000000000C001E001E000E>
	 15 36 1 27 13] 106 @dc
[<
80402010100808043C3C3C3C1C>
	 6 13 -3 4 13] 44 @dc
@F12 @sf
[<
F0001C00070003000380038003800380038003800380038003800380038003800380018001
C000E0003C00E001C001800380038003800380038003800380038003800380038003800380
030007001C00F000>
	 14 41 -3 30 21] 103 @dc

4 @eop0

0 0 4 @bop1 -58 w @F18 @sf(4)563 b(ISTV)4 -8 y(\023)-22 8 y(AN)16 b(MAR)o
(OS)-863 100 y @F20 @sf(problems.)i(Suc)o(h)12 b(problems)h(caused)h
(MINET)e(to)h(mak)o(e)f(man)o(y)f(degenerate)j(steps.)19 b(In)13 b(an)-1445 
53 y(e\013ort)e(to)f(try)h(to)f(decrease)q 12 x(the)h(n)o(um)o(b)q(er)f
(of)g(them,)h(a)f(new)h(an)o(ti{degeneracy)g(ro)o(w)f(selection)-1444 54 y
(pro)q(cedure)k(w)o(as)e(in)o(tro)q(duced)h([)p @F9 @sf(10)p @F20 @sf(])e
(and)h(exp)q(erimen)o(tally)g(implemen)o(ted)f(in)h(MINET.)g(The)-1444 54 y
(idea)i(b)q(ehind)g(it)f(can)h(brie\015y)h(b)q(e)f(sk)o(etc)o(hed)h(as)f
(follo)o(ws.)-831 63 y(During)20 b(degenerate)q 22 x(iterations)h(the)h(v)n
(alue)e(of)h(the)g(ob)r(jectiv)o(e)h(function)f(do)q(es)h(not)-1445 54 y
(c)o(hange)f(if)f(w)o(e)h(do)f(not)h(w)o(an)o(t)f(to)h(violate)f(the)h
(feasibilit)o(y)e(b)q(ounds)i(of)f(the)i(basic)f(and)-1445 54 y(the)d
(out{going)d(v)n(ariables.)26 b(On)17 b(the)h(other)g(hand,)f(the)g(ob)r
(jectiv)o(e)h(can)f(b)q(e)g(impro)o(v)o(ed)f(if)-1445 54 y(w)o(e)i(relax)g
(the)h(feasibilit)o(y)d(b)q(ounds)j(of)e(these)j(v)n(ariables)d(in)h(ev)o
(ery)h(iteration)e(and)h(allo)o(w)-1446 54 y(some)13 b(or)f(all)f(of)h
(them)h(to)f(go)g(sligh)o(tly)f(more)h(and)h(more)f(infeasible.)17 b
(Namely)m(,)11 b(this)i(alw)o(a)o(ys)-1446 53 y(allo)o(ws)g(us)i(to)f(mak)o
(e)f(a)h(p)q(ositiv)o(e)g(step,)h(at)f(least)g(to)h(the)f(exten)o(t)i(of)d
(the)i(relaxation)e(of)h(the)-1444 54 y(feasibilit)o(y)9 b(b)q(ounds.)18 b
(By)11 b(this)g(principle,)g(at)f(least)h(a)g @F4 @sf(minimum)h(for)n(c)n
(e)n(d)f(step)g @F20 @sf(can)g(b)q(e)h(made)-1445 54 y(at)17 b(eac)o(h)g
(iteration.)26 b(It)16 b(is)h(imp)q(ortan)o(t)f(that)h(the)g(v)n(alue)f
(of)g(the)h(ob)r(jectiv)o(e)h(function)e(will)-1446 54 y(alw)o(a)o(ys)f(c)o
(hange,)i(therefore,)h(a)e(past)g(basis)h(cannot)f(come)h(up)f(again,)f
(th)o(us)i(cycling)f(will)-1446 54 y(not)e(o)q(ccur.)20 b(A)o(t)15 b(the)g
(same)f(time,)g(the)g(ev)o(er)h(gro)o(wing)f(infeasibili)o(t)o(y)f(ma)o(y)g
(cause)i(troubles.)-1444 54 y(Ho)o(w)o(ev)o(er,)f(if)f(it)g(is)h(small)f
(enough,)g(it)h(can)g(b)q(e)g(k)o(ept)h(under)f(con)o(trol.)-1035 63 y
(Though)g(a)g(minim)o -1 x(um)f(forced)i(step)g(corresp)q(onds)h(to)e(an)g
(otherwise)h(degenerate)q 15 x(iter-)-1444 54 y(ation,)e(exp)q(erience)j
(has)d(sho)o(wn)h(that)g(b)o(y)g(this)g(tec)o(hnique)g(usually)f(less)i
(time)e(is)h(sp)q(en)o(t)h(on)-1445 53 y(degenerate)f(v)o(ertices)f(\(this)f
(pro)q(cedure)i(generates)f(di\013eren)o(t)g(piv)o(ot)e(sequence)q(\),)i
(therefore)-1443 54 y(the)j(o)o(v)o(erall)f(e\016ciency)h(of)f(the)h
(algorithm)e(increases.)25 b(Moreo)o(v)o(er,)16 b(since)h(w)o(e)e(kno)o(w)g
(that)-1444 54 y(the)g(solution)f(of)g(the)i(MCNF)f(problem)f(will)g(b)q
(e)h(an)f(in)o(teger)i(p)q(oin)o(t,)e(it)g(can)h(b)q(e)g(exp)q(ect)q(ed)
-1443 54 y(that)d(the)g(relaxed)g(optimal)e(solution)h(will)g(b)q(e)h(in)f
(the)i(close)f(neigh)o(b)q(orho)q(o)q(d)g(of)f(the)h(in)o(teger)-1444 54 y
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0 0 5 @bop1 353 -58 a @F18 @sf(PERF)o(ORMANC)q(E)16 b(EV)l(ALUA)q -3 x
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10 @eop0

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11 @eop0

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@F9 @sf(5.)24 b(GTE{instances)-861 78 y @F20 @sf(The)18 b(third)f
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54 y(The)d(range)g(of)g(the)g(running)g(times)g(is)f(0.020)g @F15 @sf(sec)h 
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11 @eop1

12 @bop0
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12 @eop0

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54 y(gte.15710)177 b(163)206 b(71)120 b(2869)136 b(0.04)-1075 54 y
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12 @eop1

13 @bop0
@F6 @sf
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	 18 25 -2 24 22] 71 @dc
[<
7F03C0FF87E07F07E01C0E701C0E701C0E201C0E001C0E001C0E001C0E001C1C001FFC001F
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00>
	 20 25 -1 24 22] 82 @dc
[<
7F1FC0FF1FE07F1FC01C07001C07001C07001FFF000FFE000FFE000E0E000E0E00071C0007
1C00071C00071C00071C0003180003B80003B80003B80001B00001B00001F00001F00000E0
00>
	 19 25 -1 24 22] 65 @dc
[<
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	 18 25 -1 24 22] 80 @dc
[<
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	 19 25 -1 24 22] 72 @dc
@F6 @sf
[<
1FFC003FFE007FFF00780F00F00780F00780E00380E00380E00380E00380E00380E00380E0
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	 17 25 -2 24 22] 79 @dc
[<
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	 19 25 -1 24 22] 84 @dc
@F2 @sf
[<
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	 17 29 -3 27 23] 56 @dc
@F6 @sf
[<
7F1FC0FF1FE07F1FC01C07000E0E000E0E00071C00071C0007B80003B80003F00001F00001
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	 19 25 -1 24 22] 88 @dc
@F6 @sf
[<
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	 19 25 -1 24 22] 89 @dc
@F6 @sf
[<
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	 19 25 -1 24 22] 77 @dc
[<
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	 17 25 -2 24 22] 67 @dc
@F6 @sf
[<
C7F000FFFC00FFFE00F80F00E00700E00380600380000380000380000700000F0000FE0007
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	 17 25 -2 24 22] 83 @dc
@F6 @sf
[<
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	 19 25 -1 24 22] 69 @dc
[<
7FF800FFFE007FFF001C0F801C07801C03C01C01C01C01C01C00E01C00E01C00E01C00E01C
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00>
	 19 25 0 24 22] 68 @dc

13 @eop0

0 0 13 @bop1 353 -58 a @F18 @sf(PERF)o(ORMANC)q(E)16 b(EV)l(ALUA)q -3 x
(TION)q 17 x(OF)f(MINET)319 b(13)-1395 100 y @F20 @sf(F)m(or)14 b(the)h
(comparison,)e(w)o(e)h(used)i(sev)o(en)f(of)e(the)i(eigh)o(t)f(selecte)q
(d)h(NETGEN)g(problems.)-1445 53 y(The)10 b(smallest)f(of)g(them)h(\(#11\))f
(is)g(an)h(assignmen)o(t)f(problem)h(that)f(could)h(not)f(b)q(e)h(con)o(v)o
(erted)-1443 54 y(for)i(NETFLO)h(b)o(y)f(the)h(supplied)g(con)o(v)o
(ersion)f(routine,)h(therefore)h(it)e(w)o(as)g(not)g(considered)-1443 54 y
(here.)-37 57 y(In)f(the)i(other)f(rounds)g(of)f(comparisons)h(w)o(e)g
(used)g(problem)g(classes)h(from)e(the)h(\014nal)f(DI-)-1445 54 y(MA)o(CS)i
(Core)h(problems)g([)p @F9 @sf(12)p @F20 @sf(].)o 17 x(First,)g(problems)f
(generated)i(b)o(y)e(the)h @F6 @sf(GGRAPH)e @F20 @sf(generator,)-1444 54 y
(pro)q(ducing)h(grid)f(graphs,)g(w)o(ere)h(used,)h(then)f(sev)o(eral)g
(di\013eren)o(t)g(classes)h(generated)g(b)o(y)e(the)-1444 54 y @F6 @sf
(GOTO)i @F20 @sf(generator,)g(pro)q(ducing)h(capacitated)g(transp)q
(ortation)f(problems)h(on)f(a)g(Grid{On{)-1445 54 y(TOrus)h(net)o(w)o
(ork,)e(w)o(ere)i(solv)o(ed.)j(The)c(GOTO)g(problems)g(are)h(ac)o(kno)o
(wledgedly)e(hard.)-1352 56 y(F)m(or)18 b(the)i(tests,)h(b)q(oth)e(MINET)g
(and)g(NETFLO)h(w)o(ere)g(compiled)e(with)h(the)g(recom-)-1444 54 y
(mended)c @F12 @sf(\000)p @F15 @sf(O)f @F20 @sf(optimization)f(feature)h
(of)g(the)g @F15 @sf(f)t @F20 @sf(77)g(compiler.)-931 57 y(Results)g(with)g
(the)g(selecte)q(d)h(NETGEN)f(problems)g(are)g(summarized)g(in)g(T)m(able)f
(8.)-1386 140 y 1373 -2 z 639 53 a(MINET)284 b(NETFLO)-1239 54 y(Problem)
45 b(No)q(des)i(Edges)f(Iterations)g(User)15 b(time)45 b(Iterations)h
(User)15 b(time)-1346 56 y 1373 -2 z 56 54 a(20)149 b(400)68 b(1426)136 b
(1468)168 b(1.9)136 b(1338)168 b(2.6)-1290 54 y(27)149 b(400)68 b(2676)136 b
(2323)168 b(3.3)136 b(1900)168 b(5.3)-1290 54 y(28)128 b(1000)68 b(2900)
136 b(4503)168 b(5.0)136 b(3565)168 b(7.7)-1290 54 y(32)128 b(1500)68 b
(4342)136 b(6594)168 b(8.1)136 b(5704)148 b(15.2)-1291 54 y(36)128 b(8000)
48 b(15000)115 b(34461)147 b(85.3)115 b(31246)126 b(186.0)-1291 54 y(38)i
(3000)48 b(35000)115 b(54105)147 b(79.7)115 b(25077)126 b(333.7)-1291 54 y
(40)i(3000)48 b(23000)115 b(41595)147 b(54.6)115 b(23267)126 b(195.7)-1347 
56 y 1373 -2 z 635 58 a @F2 @sf(T)l(able)17 b(8.)-760 86 y @F20 @sf(There)d
(are)e(a)h(few)f(things)h(in)f(T)m(able)g(8)g(that)h(deserv)o(e)h(atten)o
(tion.)j(First,)c(the)g(t)o(w)o(o)f(co)q(des)-1443 54 y(giv)o(e)e(di\013eren)o
(t)i(sequences)q 12 x(of)e(problems)g(if)g(sorted)i(b)o(y)e(solution)g
(time.)16 b(Second,)c(NETFLO)-1444 54 y(tends)h(to)f(mak)o(e)f
(considerably)h(less)h(iterations)f(than)g(MINET.)f(Third,)h(solution)f
(times)h(of)-1445 54 y(MINET)f(get)f(signi\014can)o(tly)f(smaller)h(than)g
(that)h(of)e(NETFLO)i(as)f(problem)g(size)h(increases)q(.)-1394 56 y(The)
16 b(GGRAPH)e(problems)i(can)f(b)q(e)h(generated)h(b)o(y)e(5)h
(parameters:)22 b @F6 @sf(X)p @F20 @sf(:)14 b(Grid)h(heigh)o(t,)-1445 54 y 
@F6 @sf(Y)p @F20 @sf(:)h(Grid)f(width,)i @F6 @sf(MAXCAP)p @F20 @sf(:)o 15 x
(Capacities)g(are)f(uniform)g(on)g([0,)f @F6 @sf(MAXCAP)p @F20 @sf(],)g 
@F6 @sf(MAXCOST)p @F20 @sf(:)o 15 x(Costs)-1444 54 y(are)f(uniform)f(on)h
([0,)e @F6 @sf(MAXCOST)p @F20 @sf(],)o 13 x @F6 @sf(SEED)p @F20 @sf(:)g
(Seed)j(of)e(the)i(random)e(n)o(um)o(b)q(er)h(generator.)-1293 57 y(F)m
(or)e(all)f(of)h(the)h(GGRAPH)e(problems)i(the)g(v)n(alues)f @F6 @sf
(MAXCAP)p @F20 @sf(=)e(10)p -15 w @F17 @sf(4)14 15 y @F20 @sf(and)i @F6 @sf
(MAXCOST)p @F20 @sf(=)e(10)p -15 w @F17 @sf(4)-1443 69 y @F20 @sf(w)o(ere)j
(\014xed.)18 b(In)13 b(T)m(able)e(9,)h(under)h(problem)g(generation)f
(parameters,)h(w)o(e)g(giv)o(e)f(the)h(v)n(alues)-1445 54 y(for)h @F6 @sf
(X)p @F20 @sf(,)f @F6 @sf(Y)p @F20 @sf(,)g(and)h @F6 @sf(SEED)p @F20 @sf
(.)-289 56 y(The)c(last)f(t)o(w)o(o)g(GGARPH)g(problems)g(in)g(T)m(able)g
(9)g(di\013er)h(only)f(in)g(the)h(v)n(alue)f(of)g(the)h @F6 @sf(SEED)p 
@F20 @sf(.)-1446 54 y(F)m(or)k(this)h(set)g(w)o(e)g(ignore)f(regression)i
(analysis)d(b)q(ecause)q 16 x(the)i(problems)f(are)h(structurally)-1444 
54 y(inhomogeneous.)i(Nev)o(erthe)q(less,)d(it)f(is)g(in)o(teresting)g(to)g
(observ)o(e)h(that)f(b)q(oth)g(solv)o(ers)h(sho)o(w)-1445 54 y(a)i(smo)q
(oth)f(p)q(erformance)i(in)f(the)g(sense)q 17 x(that)g(solution)f(times)h
(increase)i(smo)q(othly)d(with)-1445 54 y(problem)f(size.)k(NETFLO)d(is)f
(alw)o(a)o(ys)e(faster)j(b)o(y)f(a)f(narro)o(w)h(margin.)-1106 54 y
13 @eop1

14 @bop0
@F2 @sf
[<
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00380E001C1C000FF80003E000>
	 17 29 -3 27 23] 57 @dc
@F6 @sf
[<
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C0>
	 19 25 -1 24 22] 78 @dc
@F15 @sf
[<
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	 40 28 -2 27 40] 77 @dc
@F15 @sf
[<
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	 33 28 -2 27 33] 78 @dc
@F2 @sf
[<
03E0000E38001C1C00380E00380E00700700700700700700F00780F00780F00780F00780F0
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	 17 29 -3 27 23] 48 @dc

14 @eop0

0 0 14 @bop1 -58 w @F18 @sf(14)545 b(ISTV)4 -8 y(\023)-22 8 y(AN)16 b(MAR)o
(OS)-863 102 y 1476 -2 z 27 53 a @F20 @sf(Generation)514 b(MINET)284 b
(NETFLO)-1315 54 y(parameters)74 b(No)q(des)47 b(Edges)f(Iterations)g
(User)15 b(time)45 b(Iterations)h(User)15 b(time)-1449 56 y 1476 -2 z 21 
54 a(32)e(32)g(270001)72 b(1026)d(2048)135 b(2674)169 b(3.5)135 b(1869)169 b
(3.0)-1450 54 y(16)13 b(128)g(270001)72 b(2050)d(3984)135 b(4988)169 b
(8.8)135 b(2282)169 b(5.9)-1450 54 y(128)13 b(16)g(270001)72 b(2050)d
(4208)135 b(5762)169 b(9.3)135 b(6260)169 b(8.9)-1429 54 y(64)13 b(64)g
(270003)72 b(4098)d(8192)115 b(13645)147 b(23.3)115 b(10168)147 b(18.8)-1450 
54 y(256)13 b(16)g(270001)72 b(4098)d(8432)115 b(12290)147 b(25.8)115 b
(13210)147 b(22.5)-1429 53 y(80)13 b(80)g(270004)72 b(6402)48 b(12800)115 b
(19539)147 b(42.2)115 b(21384)147 b(40.8)-1450 54 y(512)13 b(16)g(270001)
72 b(8194)48 b(16680)115 b(23815)147 b(77.1)115 b(33306)147 b(75.2)-1450 
54 y(512)13 b(16)g(270011)72 b(8194)48 b(16680)115 b(22811)147 b(75.9)115 b
(34968)147 b(74.4)-1450 56 y 1476 -2 z 635 54 a @F2 @sf(T)l(able)17 b(9.)
-760 105 y @F20 @sf(The)c(GOTO)h(problems)f(are)g(generated)i(b)o(y)e
(follo)n(wing)e(5)i(parameters:)19 b @F6 @sf(N)p @F20 @sf(:)12 b(Num)o(b)q
(er)i(of)-1445 54 y(no)q(des,)f @F6 @sf(M)p @F20 @sf(:)f(Num)o(b)q(er)h
(of)f(arcs,)h @F6 @sf(MAXCAP)p @F20 @sf(:)e(Maxim)o(um)g(capacit)o(y)h
(\(some)h(arcs)g(ma)o(y)f(b)q(e)h(gener-)-1444 54 y(ated)g(with)g
(capacities)h(greater)g(than)f(this)g(to)g(ensure)i(feasibilit)o(y\),)o 
12 x @F6 @sf(MAXCOST)p @F20 @sf(:)c(Maxim)o(um)-1446 54 y(arc)j(cost,)g 
@F6 @sf(SEED)p @F20 @sf(:)f(Seed)i(for)e(random)h(n)o(um)o(b)q(er)g
(generator.)-875 54 y(W)m(e)j(in)o(v)o(estigated)g(three)h(groups)g(of)e
(GOTO)i(problems.)28 b(Eac)o(h)17 b(of)g(them)g(con)o(tained)-1444 54 y
(structurally)23 b(similar)e(problems)i(on)f(whic)o(h)h(b)q(oth)f(co)q
(des)i(ob)q(ey)o(ed)f(the)h(\(3.1\))d(mo)q(del.)-1445 54 y(Therefore,)c(w)o
(e)f(could)g(use)g(regress)q(ion)g(analysis)f(for)h(comparison.)23 b(It)
16 b(turned)h(out)e(that)-1444 54 y(the)f(computed)g(v)n(alues)g(of)f(the)h
(correlation)g(co)q(e\016cien)o(ts)h(for)e(MINET)h(and)g(NETFLO)g(in)-1445 
54 y(the)j(groups)g(w)o(ere)h(quite)e(the)i(same)e(that)h(established)g(a)g
(basis)f(for)h(comparison)f(of)g(the)-1444 54 y(regression)f(lines.)-235 
54 y(The)f(\014rst)h(group)f(of)g(GOTO)g(problems)g(is)g(referenc)q(ed)i
(as)e(Grid{Densit)o(y{8,)e(\(GD{8\))-1445 54 y(and)18 b(has)g(the)g
(feature)h(that)f @F15 @sf(M)23 b @F20 @sf(=)18 b(8)p @F15 @sf(N)5 b 
@F20 @sf(.)30 b(F)m(or)18 b(the)g(generated)h(test)g(problems)f(the)h
(last)-1445 54 y(three)f(parameters,)f(in)f(all)f(cases,)i(w)o(ere)g
(\014xed:)23 b @F6 @sf(MAXCAP)p @F20 @sf(=16384,)o 16 x @F6 @sf(MAXCOST)p 
@F20 @sf(=40)o(96,)o 16 x(and)-1445 54 y @F6 @sf(SEED)p @F20 @sf(=270001)o
(.)17 b(Results)d(of)g(the)g(test)h(are)f(summarized)g(in)g(T)m(able)f
(10.)-1137 110 y 1175 -2 z 441 53 a(MINET)284 b(NETFLO)-1041 54 y(No)q
(des)46 b(Edges)h(Iterations)e(User)15 b(time)46 b(Iterations)f(User)15 b
(time)-1147 56 y 1175 -2 z 49 54 a(128)68 b(1024)136 b(1409)168 b(1.6)136 b
(2138)168 b(1.8)-1099 54 y(256)68 b(2048)136 b(3188)168 b(3.8)136 b(5450)
168 b(4.7)-1099 54 y(512)68 b(4096)136 b(6860)147 b(11.8)115 b(16496)147 b
(16.5)-1120 54 y(1024)68 b(8192)115 b(11674)147 b(41.9)115 b(30003)147 b
(54.8)-1120 54 y(2048)47 b(16384)115 b(28759)127 b(108.1)114 b(67287)127 b
(182.7)-1121 54 y(4096)47 b(32768)115 b(75322)127 b(329.3)94 b(342391)126 b
(905.9)-1149 56 y 1175 -2 z 404 54 a @F2 @sf(T)l(able)17 b(10.)-552 79 y 
@F20 @sf(The)i(second)h(group)e(of)g(GOTO)h(problems)g(is)g(called)f
(Grid{Densit)o(y{16)f(\(GD{16\),)-1446 b
14 @eop1

15 @bop0
@F12 @sf
[<
4000C000C000C000C000C000C000C000C000C000C000C000C000C000C000C000C000C000C0
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	 10 42 -7 30 18] 100 @dc
@F13 @sf
[<
C000C000C0006000600060003000300030001800180018000C000C000C0006000600030003
00030001800180018000C000C000C0006000600020>
	 11 29 -2 21 17] 61 @dc
@F12 @sf
[<
004000C000C000C000C000C000C000C000C000C000C000C000C000C000C000C000C000C000
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	 10 42 0 30 18] 101 @dc
@F20 @sf
[<
1FC03838700CF00EF01EF01EF00C7000780038001C000C0006000600060006000600030003
000200000000000000000007000F800F800F800700>
	 15 29 -2 20 20] 62 @dc

15 @eop0

0 0 15 @bop1 353 -58 a @F18 @sf(PERF)o(ORMANC)q(E)16 b(EV)l(ALUA)q -3 x
(TION)q 17 x(OF)f(MINET)319 b(15)-1445 100 y @F20 @sf(and)19 b(is)h(c)o
(haracterized)h(b)o(y)e(the)h(relation)f @F15 @sf(M)25 b @F20 @sf(=)d(16)p 
@F15 @sf(N)5 b @F20 @sf(.)34 b(The)19 b(v)n(alue)g(of)g(the)h(last)f
(three)-1443 53 y(parameters,)j(in)e(all)e(cases,)23 b(w)o(ere)e(\014xed)f
(in)g(the)g(same)h(w)o(a)o(y)e(as)h(in)g(Grid{Densit)o(y{16.)o -1446 54 a
(Results)14 b(of)g(the)g(test)h(are)f(presen)o(te)q(d)h(in)f(T)m(able)f
(11.)-818 56 y 1175 -2 z 441 54 a(MINET)284 b(NETFLO)-1041 54 y(No)q(des)
46 b(Edges)h(Iterations)e(User)15 b(time)46 b(Iterations)f(User)15 b(time)
-1147 56 y 1175 -2 z 49 54 a(128)68 b(2048)136 b(2858)168 b(3.2)136 b
(5750)168 b(4.5)-1099 54 y(256)68 b(4096)136 b(6812)168 b(8.4)115 b(14265)
147 b(11.0)-1099 53 y(512)68 b(8192)115 b(14948)147 b(24.2)115 b(31305)147 b
(30.4)-1120 54 y(1024)47 b(16384)115 b(29753)147 b(77.0)115 b(72282)127 b
(109.3)-1121 54 y(2048)47 b(32768)115 b(70538)127 b(239.4)94 b(172723)126 b
(408.3)-1121 54 y(4096)47 b(65536)95 b(143122)105 b(1042.4)94 b(460458)105 b
(1759.5)-1149 56 y 1175 -2 z 404 51 a @F2 @sf(T)l(able)17 b(11.)-552 77 y 
@F20 @sf(The)12 b(third)h(group)f(of)f(GOTO)i(problems)f(is)g(reference)q
(d)i(as)e(Grid{Increasing{Densi)p(t)o(y)-1445 54 y(\(GDI\),)i(and)g(has)h
(the)h(feature)f(that)g @F15 @sf(M)j @F20 @sf(=)13 b @F12 @sf(d)p @F15 @sf
(N)5 -15 y @F17 @sf(3)p @F13 @sf(=)p @F17 @sf(2)1 15 y @F12 @sf(e)p @F20 @sf
(.)21 b(The)16 b(rest)g(of)e(the)h(parameters)h(is)e(as)-1444 54 y(ab)q(o)o
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46 b(Edges)h(Iterations)e(User)15 b(time)46 b(Iterations)f(User)15 b(time)
-1147 48 y 1175 -2 z 49 45 a(128)68 b(1449)136 b(2040)168 b(2.2)136 b
(2725)168 b(2.5)-1099 46 y(256)68 b(4096)136 b(6812)168 b(8.4)115 b(14265)
147 b(11.0)-1099 45 y(512)47 b(11586)115 b(19490)147 b(37.0)115 b(48493)
147 b(50.7)-1120 46 y(1024)47 b(32768)115 b(60980)127 b(166.1)94 b(190027)
126 b(297.4)-1121 46 y(2048)47 b(92682)95 b(199899)126 b(832.7)94 b
(680137)105 b(1953.9)-1149 47 y 1175 -2 z 404 51 a @F2 @sf(T)l(able)17 b
(12.)-552 77 y @F20 @sf(>F)m(rom)d(T)m(ables)i(10{11{12)o 15 x(w)o(e)g
(can)f(compute)i(linear)e(regression)i(data)e(for)h(the)g(three)-1443 54 y
(GOTO)k(groups)g(b)o(y)f(\(3.1\).)36 b(The)20 b(obtained)f(v)n(alues)h(of)f 
@F15 @sf(r)i @F20 @sf(and)e @F15 @sf(b)h @F20 @sf(are)g(summarized)g(in)
-1445 54 y(T)m(able)13 b(13.)-168 94 y 814 -2 z 45 w(Group)56 b(P)o
(arameter)k(MINET)49 b(NETFLO)-785 48 y 814 -2 z 45 w(GD{8)149 b @F15 @sf
(r)131 b @F20 @sf(0.996360)o 65 x(0.998699)o -530 46 a @F15 @sf(b)g @F20 @sf
(2.406176)o 65 x(6.731219)o -787 45 a(GD{16)d @F15 @sf(r)j @F20 @sf
(0.999618)o 65 x(0.999803)o -530 46 a @F15 @sf(b)g @F20 @sf(3.856446)o 65 x
(6.540692)o -787 46 a(GDI)176 b @F15 @sf(r)131 b @F20 @sf(0.999784)o 65 x
(0.999698)o -530 45 a @F15 @sf(b)g @F20 @sf(4.352572)o 44 x(10.330800)o 
-787 48 a 814 -2 z 286 51 a @F2 @sf(T)l(able)17 b(13.)-434 100 y @F20 @sf
(Based)f(on)g(the)g(near)g(equalit)o(y)f(of)g(the)h(correlation)f(co)q
(e\016cien)o(ts)i(\()p @F15 @sf(r)q @F20 @sf(\))f(of)f(MINET)h(and)-1445 b
15 @eop1

16 @bop0
@F9 @sf
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@F20 @sf
[<
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	 15 29 -2 28 20] 63 @dc
@F6 @sf
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	 17 25 -2 24 22] 50 @dc

16 @eop0

0 0 16 @bop1 -58 w @F18 @sf(16)545 b(ISTV)4 -8 y(\023)-22 8 y(AN)16 b(MAR)o
(OS)-863 100 y @F20 @sf(NETFLO)e(in)e(T)m(able)g(13,)g(w)o(e)i(can)f
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(Running)14 b(times)i(v)o(ersus)e(loading)i(conditions)o 15 x(of)f(the)g
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(of)-1445 54 y(an)e(iteration)f(can)h(b)q(e)h(di\013eren)o(t)g(from)e
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(program)g(w)o(as)h(b)q(eliev)o(ed)g(to)g(b)q(e)g(prop)q(ortional)f(to)g
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(e)h(a)f(problem)h(and)g(therefore)h(suitable)e(for)h(com-)-1445 54 y
(paring)h(the)h(p)q(erformance)h(of)d(di\013eren)o(t)j(algorithms.)j
(Standards)c(ha)o(v)o(e)f(b)q(een)i(set)f(up)g(for)-1445 54 y(rep)q
(orting)f(computational)f(exp)q(eriences)q 15 x(\(c.f.,)g([)p @F9 @sf(1)p 
@F20 @sf(])g(or)g([)p @F9 @sf(4)p @F20 @sf(]\).)-908 55 y(Timing)d(on)h
(PCs)h(is)f(relativ)o(ely)f(simple)h(and)g(accurate.)19 b(F)m(or)11 b
(comparabili)o(t)o(y)f(of)h(results,)-1444 54 y(it)16 b(is)g(more)g(or)g
(less)h(su\016cien)o(t)f(to)g(sp)q(ecify)h(the)g(t)o(yp)q(e)f(of)g(the)g
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(the)i @F4 @sf(solution)g(time)e @F20 @sf(whic)o(h)h(is)g(usually)f(equal)g
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(orkstations,)d(ho)o(w)o(ev)o(er,)h(run)h(under)f(UNIX)h(op)q(erating)f
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(er)g(of)f(programs)g(ma)o(y)g(run)h(in)f(the)i(computer.)27 b(This)16 b
(immediately)f(ex-)-1444 54 y(plains)g(wh)o(y)g(the)h(question)f(of)g
(timing)f(accuracy)i(w)o(as)f(raised)h(b)o(y)f(the)h(organizers)g(of)f
(the)-1444 54 y(First)f(DIMA)o(CS)g(In)o(ternational)f(Algorithm)g
(Implemen)o(tation)f(Challenge)i([)p @F9 @sf(11)p @F20 @sf(].)-1257 55 y
(Clearly)m(,)d(under)i(UNIX)g(en)o(vironmen)o(t,)g(residence)h(time)e(can)h
(b)q(e)g(an)o(ything)f(dep)q(ending)-1444 54 y(on)h(the)g(nature)h(of)f
(the)g(concurren)q -1 x(tly)g(running)g(pro)q(cess)q(es,)i(therefore)f(it)f
(cannot)g(b)q(e)h(used)-1444 54 y(for)g(timing.)19 b(Ho)o(w)o(ev)o(er,)14 b
(most)g(of)g(the)h(systems)h(o\013er)f(time)f(measuring)h(pro)q(cedures)q 
15 x(that)-1444 54 y(can)f(separate)h @F4 @sf(system)g(time)e @F20 @sf
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(estigated)h(with)f(MINET)h(the)g(follo)o(wing)o 19 x(question:)29 b(Ho)o
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(MINET)20 b(uses)h(the)g @F4 @sf(etime)f @F20 @sf(routine)g(of)f(the)i
(UNIX)f(F)o(OR)m(TRAN)f(library)m(.)35 b(Its)21 b(\014rst)-1444 54 y
(parameter)15 b(is)e(supp)q(osed)i(to)f(measure)h(user)g(time.)-763 55 y
(First,)g(the)h(p)q(erformance)g(of)f @F4 @sf(etime)g @F20 @sf(w)o(as)g
(tested)i(when)f(the)g(Spark)f(1+)g(w)o(as)g(run)h(in)f(a)-1445 53 y
(stand)j(alone)e(mo)q(de.)29 b(The)17 b(problem)g(to)g(b)q(e)h(solv)o(ed)f
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(iden)o(ti\014ed)h(as)f @F6 @sf(gg2)f @F20 @sf(with)h(2027)g(no)q(des)h
(and)f(4050)f(arcs.)18 b(MINET)c(solv)o(ed)f @F6 @sf(gg2)-1445 54 y @F20 @sf
(three)i(consecutiv)o(e)h(times)d(in)h(7.82,)e(7.73,)g(and)i(7.79)f
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54 y(w)o(ork)o(ed)g(on)f @F6 @sf(gg2)g @F20 @sf(concurren)o(tly)m(,)h(the)g
(follo)o(wi)o(ng)e(running)h(times)h(w)o(ere)h(obtained)e(at)g(tree)-1443 
54 y(di\013eren)o(t)g(attempts:)-337 81 y(Run)69 b(Cop)o(y{A)f(Cop)o(y{B)
-478 54 y(1)133 b(7.80)140 b(7.87)-444 54 y(2)133 b(7.75)140 b(7.89)-444 
54 y(3)133 b(7.84)140 b(7.88)-422 81 y(When)12 b(the)h(exp)q(erimen)o(t)g
(w)o(as)e(rep)q(eate)q(d)i(with)f(three)h(copies)g(of)e(MINET)i(running)e
(con-)-1444 b
16 @eop1

17 @bop0
@F20 @sf
[<
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	 14 1 -3 24 21] 22 @dc
@F15 @sf
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[<
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[<
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	 15 13 -1 12 17] 120 @dc
@F15 @sf
[<
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@F17 @sf
[<
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	 7 21 -1 20 9] 105 @dc
[<
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	 15 13 -1 12 18] 110 @dc
@F6 @sf
[<
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17 @eop0

0 0 17 @bop1 353 -58 a @F18 @sf(PERF)o(ORMANC)q(E)16 b(EV)l(ALUA)q -3 x
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@F4 @sf(etime)g @F20 @sf(w)o(ere)i(7.62,)e(7.70,)g(and)h(7.67)-1446 53 y
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(time)-1445 54 y(of)f(a)h(program,)f(and)g(not)h(residence)q 15 x(time)g
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(ev)o(eryda)o(y)-1444 54 y(m)o(ultiprogramm)o(ing,)o 13 x(m)o
(ultitasking,)f(and)h(net)o(w)o(orking)g(circumstances)q(,)h(w)o(e)g
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(In)o(terv)n(al)712 b(\()s(\026)-24 b @F15 @sf(x)p @F20 @sf(\))151 b(%)-1094 
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@F15 @sf(=t)p 6 w @F17 @sf(min)-1159 40 y @F20 @sf(In)o(terv)n(al)696 b(\()s
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17 @eop1

18 @bop0

18 @eop0
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(OS)-863 100 y 1053 -2 z 45 w @F20 @sf(Time)114 b(Observ)n(ations)14 b(\()p 
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6 w @F17 @sf(max)3 -6 y @F15 @sf(=t)p 6 w @F17 @sf(min)-1037 40 y @F20 @sf
(In)o(terv)n(al)583 b(\()s(\026)-24 b @F15 @sf(x)p @F20 @sf(\))151 b(%)-965 
47 y 1053 -2 z 46 w(3)14 b(min)104 b(8.14)12 b(8.17)h(8.20)g(7.85)158 b
(8.090)109 b(104.46)-1027 45 y(3)14 b(min)104 b(9.70)12 b(9.51)h(9.46)g
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(8.18)h(8.17)g(9.20)158 b(8.860)109 b(121.05)-1027 48 y 1053 -2 z 209 45 a
(T)m(otal)399 b(8.898)109 b(125.99)-1027 48 y 1053 -2 z 404 79 a @F2 @sf
(T)l(able)17 b(16.)-552 106 y @F20 @sf(The)f(obtained)g(\014gures)h(do)f
(not)g(lo)q(ok)f(v)o(ery)i(encouraging.)24 b(Running)16 b(times)g(seem)h
(to)-1445 54 y(v)n(ary)c(to)q(o)h(m)o(uc)o(h.)k(A)c(bit)f(more)h(careful)g
(analysis)f(rev)o(eals)i(some)f(imp)q(ortan)o(t)f(details.)-1313 54 y
(Within)f(the)h(\014rst)h(four)f(ro)o(ws)g(of)g @F6 @sf(gg2)f @F20 @sf(\(T)m
(able)g(14\))h(w)o(e)g(can)g(see)i(a)d(uniform)g(b)q(eha)o(vior)h(of)-1445 
54 y(running)e(times.)18 b(The)12 b(same)g(uniform)e(\014gures)j(cannot)f
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12 b(v)n(alues)g(of)f(7.940,)f(7.650,)h(8.174,)o 11 x(and)h(9.700)f(di\013er)h
(nearly)g(27%.)17 b(Then)12 b(comes)h(ro)o(w)-1445 54 y(5)g(with)f(a)h(v)o
(ery)g(inhomogeneous)g(ro)o(w)f(p)q(erformance)i(and)f(globall)o(y)f
(extreme)i(v)n(alues)e(that)-1444 54 y(also)h(de\014ne)i(the)g @F15 @sf(t)p 
6 w @F17 @sf(max)2 -6 y @F15 @sf(=t)p 6 w @F17 @sf(min)17 -6 y @F20 @sf
(ratio)e(for)g(the)i(whole)f(sample.)-899 54 y(The)f(same)f(can)h(b)q(e)g
(said)f(if)g(w)o(e)h(lo)q(ok)e(at)h(the)h(observ)o(ed)h(data)e(for)g @F6 @sf
(gg3)g @F20 @sf(\(T)m(able)g(15\).)17 b(The)-1444 54 y(only)12 b
(di\013erence)i(is)e(that)h(in)f(this)g(case)i(the)f(v)n(ariable)e(b)q
(eha)o(vior)h(can)h(b)q(e)g(seen)h(in)e(t)o(w)o(o)g(ro)o(ws.)-1395 55 y
(Though)h(in)f(the)i(third)f(series)i(of)d(observ)n(ations)h @F6 @sf(cap1)g 
@F20 @sf(\(T)m(able)f(16\))h(did)g(not)g(sho)o(w)g(suc)o(h)-1444 54 y(a)h
(more)f(than)h(40%)f(deviation,)g(it)g(is)h(still)f(to)q(o)h(v)n(ariable)e
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(single)g(coun)o(terexample)h(can)g(b)q(e)g(found)f(then)h(this)f(is)h
(su\016-)-1445 54 y(cien)o(t)e(to)g(reject)h(the)f(unconditional)e
(reliabilit)o(y)g(of)h(time)h(measuring)f(in)g(UNIX.)h(What)f(w)o(e)-1444 
54 y(presen)o(te)q(d)i(here)f(is)f(de\014nitely)h(more)f(than)h(just)f(a)h
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(imagi)o(ne)e(a)h(long)g(test)h(run)g(including)e(the)i(serial)f(solution)g
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(the)g(comparabilit)o(y)-1446 54 y(of)g(suc)o(h)i(solution)e(times.)-357 
54 y(Ha)o(ving)g(seen)i(the)f(ab)q(o)o(v)o(e)g(instances)h(sev)o(eral)f
(questions)h(can)f(b)q(e)g(ask)o(ed.)19 b(What)13 b(is)h(the)-1444 54 y
(real)k(solution)e(time?)29 b(Ho)o(w)18 b(can)g(w)o(e)f(compare)h
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(times?)18 b(W)m(e)11 b(think)g(that)h(no)o(w)o(ada)o(ys,)f(when)h(a)f
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(algorithm)e(is)i(considered)i(signi\014can)o(t,)e(these)i(questions)f
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(ose)g(here)h(is)e(to)g(p)q(oin)o(t)g(out)g(the)h(ab)q(o)o(v)o(e)f
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(considerable)h(e\013ort.)22 b(A)o(t)15 b(the)g(same)g(time,)f(it)g(app)q
(ears)i(inevitable)e(that)h(suc)o(h)-1444 54 y(a)f(study)g(m)o(ust)g(b)q
(e)g(conducted.)88 106 y @F9 @sf(8.)24 b(Summary)-804 79 y @F20 @sf(Based)
18 b(on)f(the)h(quic)o(k)f(o)o(v)o(erview)g(of)g(the)h(ab)q(o)o(v)o(e)f
(exp)q(erience)q(s,)i(it)e(can)h(b)q(e)g(concluded)-1444 54 y(that)13 b
(MINET)h(sho)o(ws)f(a)g(relativ)o(ely)g(stable)g(and)g(more)h(or)f(less)h
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(setting)e(of)f(the)i(a)o(v)n(ail)o(abl)o(e)e(strategic)i(parameters.)-1067 
54 y(In)e(the)h(discussion)f(|)g(among)f(others)i(|)e(w)o(e)h(addresse)q
(d)h(t)o(w)o(o)f(imp)q(ortan)o(t)f(issues)i(that)-1444 54 y(ma)o(y)j
(in\015uence)i(the)g(comparabilit)o(y)d(of)h(rep)q(orte)q(d)i(running)f
(times)g(and,)g(therefore)i(the)-1444 b
18 @eop1

19 @bop0
@F9 @sf
[<
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	 31 28 -2 27 36] 65 @dc
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	 22 29 -1 28 25] 107 @dc
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[<
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	 22 21 -1 20 25] 114 @dc
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[<
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	 13 21 -2 20 19] 115 @dc
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[<
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	 16 23 0 22 18] 74 @dc
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	 14 17 -1 16 18] 102 @dc
[<
87E0D810E008C0048006800680060006000E001C01FC0FF83FE07F007000E000C004C004C0
04400C601C306C0F84>
	 15 23 -2 22 21] 83 @dc
[<
FFFF80>
	 17 1 0 8 19] 123 @dc
[<
FFE007000700070007000700070007000700070007000700070007000700070007000700F7
000F000300>
	 11 21 -3 20 19] 49 @dc
[<
1F0020C040608030E038E0384038003800380030207030602F80200020002000200022003F
C03FE03030>
	 13 21 -2 20 19] 53 @dc
[<
0F8030606030C010C018C018C018C038607031F01FE01F803EC03C60703060306030603020
6010C00F80>
	 13 21 -2 20 19] 56 @dc
[<
FFFF001C01C01C00E01C00701C00381C00381C00381C00381C00301C00701C00E01FFFC01F
FF801C01C01C00E01C00701C00701C00701C00701C00601C00E01C0380FFFE00>
	 21 23 -2 22 27] 66 @dc
[<
FF80001C00001C00001C00001C00001C00001C00001C00001C00001C00001C00001FFE001C
03801C00C01C00E01C00701C00701C00701C00701C00E01C00C01C0380FFFE00>
	 20 23 -2 22 26] 80 @dc
[<
00FF000381C00E00701C003838001C38001C70000E70000EE00007E00007E00007E00007E0
0007E00007E0000760000670000E30000C1800181C00380600600381C0007E00>
	 24 23 -2 22 30] 79 @dc
[<
F81F80300E00100C000818000C380004300002600001C00001C00001800003400007600006
20000C1000180800181C00FC1F00>
	 17 17 -1 16 21] 120 @dc
[<
0F8018C03060703060386038E038E038E038E030F070E860E780E000600070003038303818
180C1003E0>
	 13 21 -2 20 19] 54 @dc
[<
0F8030E04070C030E038E038003800380030007000E00F8001C000E0006000707070707060
6030C00F80>
	 13 21 -2 20 19] 51 @dc
@F18 @sf
[<
60F0F06000000000000060F0F060>
	 4 14 -3 13 10] 58 @dc
[<
FFFF00FFFFC01E01E01E00F01E00781E00781E00781E00781E00781E00F01E01E01FFFC01F
FF801E01C01E01E01E00F01E00F01E00F01E00F01E01E01E03E0FFFF80FFFF00>
	 21 23 -1 22 25] 66 @dc
@F18 @sf
[<
00FF000300F00C001C1800003078E030CD9861878863838CC3038CC7038CC7038CC7038CC7
038CC7038CC3038C63839861861830CC303078301800600C00C003030000FC00>
	 22 23 -2 22 27] 64 @dc

19 @eop0

0 0 19 @bop1 353 -58 a @F18 @sf(PERF)o(ORMANC)q(E)16 b(EV)l(ALUA)q -3 x
(TION)q 17 x(OF)f(MINET)319 b(19)-1445 100 y @F20 @sf(relativ)o(e)18 b
(e\016ciency)i(of)d(co)q(des.)33 b(It)19 b(turned)g(out)g(that)f(the)h
(optimizing)e(capabilit)o(y)g(of)h(a)-1445 53 y(compiler)e(can)g(impro)o
(v)o(e)f(timings)g(b)o(y)h(more)g(than)g(40%.)24 b(It)16 b(also)g(b)q
(ecame)h(eviden)o(t)f(that)-1444 54 y(time)h(measuring)f(under)i(UNIX)f
(op)q(erating)g(system)g(can)g(b)q(e)h(rather)g(unreliable)e(giving)-1446 
54 y(an)f(at)g(least)h(40%)e(wide)i(range)f(of)g(solution)g(times.)22 b
(The)16 b(former)f(observ)n(ation)g(suggests)-1443 54 y(that)d
(information)e(on)i(co)q(de)h(optimization)d(m)o(ust)i(alw)o(a)o(ys)f(b)q
(e)i(pro)o(vided,)f(while)g(the)g(latter)-1444 54 y(necess)q(itates)j(an)f
(in{depth)g(analysis)f(of)g(time)h(measuring)g(in)f(UNIX.)-615 104 y @F9 @sf
(9.)24 b(Ac)o(kno)o(wledgmen)o -1 x(ts)-892 79 y @F20 @sf(The)15 b(author)f
(is)h(indebted)g(to)g(the)g(t)o(w)o(o)f(anon)o(ymous)g(referees)q 16 x
(for)g(their)h(helpful)f(com-)-1445 54 y(men)o(ts.)482 104 y @F2 @sf
(References)-824 66 y @F18 @sf(1.)j(Cro)o(wder,)f(Dem)o(b)q(o,)g(and)f
(Mulv)o(ey,)g @F3 @sf(R)n(ep)n(orting)j(Computational)f(Exp)n(erime)q(nts)g
(in)g(Mathematic)n(al)-1380 42 y(Pr)n(o)n(gr)n(amming)p @F18 @sf(,)d
(Mathematic)o(al)c(Programming)g @F8 @sf(15)i @F18 @sf(\(1978\),)e(315{32)o
(9.)-1027 41 y(2.)17 b(Cunningh)o(am,)9 b(W.)h(H.,)g @F3 @sf(The)n(or)n
(etic)n(a)q(l)i(Pr)n(op)n(erties)h(of)e(the)h(Network)g(Simplex)g(Metho)n
(d)p @F18 @sf(,)f(Mathematics)-1383 42 y(of)g(Op)q(eration)o(s)f(Researc)o
(h)g @F8 @sf(4)i @F18 @sf(\(1979\),)e(196{20)o(8.)-702 41 y(3.)17 b(Gal,)
10 b(T.,)i(Geue,)e(F.,)h @F3 @sf(A)i(New)g(Pivoting)g(R)o(ule)h(for)e
(Solving)i(V)m(arious)f(De)n(gene)q(r)n(acy)q 14 x(Pr)n(oblems)p @F18 @sf
(,)f(Op)q(er-)-1382 42 y(ations)e(Researc)o(h)o 11 x(Letters)g @F8 @sf(11)i 
@F18 @sf(\(1992\),)e(23{32.)o -689 41 a(4.)17 b(Green)o(b)o 1 x(erg)o(,)
10 b(H.)j(J.,)e @F3 @sf(Computational)j(T)m(esting:)i(Why,)d(How,)g(and)g
(How)h(Much)p @F18 @sf(,)e(ORSA)g(Journal)e(on)-1382 42 y(Computing)g 
@F8 @sf(2)i @F18 @sf(\(1990\),)o 11 x(94{97)o(.)-480 41 y(5.)17 b
(Klingman,)f(D.,)i(Napier,)e(A.,)i(Stutz,)o 17 x(J.,)f @F3 @sf(NETGEN|A)i
(pr)n(o)n(gr)n(am)g(for)e(gener)n(ating)i(lar)n(ge{sc)n(a)q(le)-1380 42 y
(\(un\)c)n(ap)n(acitate)n(d)g(assignment,)f(tr)n(ansp)n(ortation)f(and)h
(minimum)f(c)n(ost)h(\015ow)f(pr)n(oblems)p @F18 @sf(,)h(Manage-)-1383 41 y
(men)o(t)11 b(Scienc)o(e)f @F8 @sf(20)j @F18 @sf(\(1974\))o(,)d(814{821)o
(.)-564 42 y(6.)17 b(Lo)o(v)o(e,)d(R.)h(R.,)g @F3 @sf(T)m(r)n(a\016c)i
(sche)n(duling)g(via)f(Benders)g(de)n(c)n(o)q(mp)n(osition)p @F18 @sf(,)h
(Mathematic)o(al)c(Programming)-1383 41 y(Study)o 11 x @F8 @sf(15)f @F18 @sf
(\(1981\),)o 11 x(102{1)o(24.)o -454 42 a(7.)17 b(Maros,)10 b(I.,)h @F3 @sf
(MINET)h(a)g(F)m(ast)h(Network)g(LP)g(Solver)p @F18 @sf(,)f(I)q(IASA)f(W)m
(orking)f(P)o(ap)q(er)g(WP{87{50)o(,)g(In)o(terna)o(-)-1383 41 y(tional)o 
11 x(Institu)o(te)g(for)h(Applied)f(Systems)h(Analysis,)f(A{2361)g(Laxen)o
(burg)o(,)g(Austria,)h(1987.)-1293 42 y(8.)17 b(Maros,)f(I.,)h @F3 @sf
(MINET)f(F)m(ast)h(Network)h(LP)g(Solver,)h(Description)e(and)h(User's)e
(Guide)i(for)f(V2.00)p @F18 @sf(,)-1381 41 y(I)q(IASA)e(W)m(orking)g(P)o
(ap)q(er)f(WP{88{6,)i(In)o(ter)o(nat)o(ion)o(al)e(Institute)o 15 x(for)h
(Applied)f(Systems)h(Analysis,)-1383 42 y(A{2361)10 b(Laxen)o(bu)o(rg,)g
(Austria,)g(1988.)-574 41 y(9.)17 b(Maros,)10 b(I.,)g @F3 @sf(A)i
(Structur)n(e)h(Exploiting)g(Pricing)g(Pr)n(o)n(c)n(e)o(dur)n(e)q 13 x(in)f
(the)g(Primal)h(Network)f(Simplex)i(A)o(lgo-)-1381 42 y(rithm,)p @F18 @sf
(,)d(R)o(UTCO)q(R)i(Researc)o(h)o 11 x(Rep)q(ort)o(,)e(RRR)g(#18{91,)f(R)o
(UTCO)q(R,)j(Rutgers)o 11 x(Univ)o(ersit)o(y)o(,)d(1991.)-1425 41 y(10.)
17 b(Maros,)10 b(I.,)h @F3 @sf(A)h(Pr)n(actic)n(al)i(A)o(nti{De)n(gene)q
(r)n(ac)q(y)g(R)n(ow)e(Sele)n(ction)i(T)m(e)n(chnique)g(in)e(Network)h
(Line)n(ar)g(Pr)n(o-)-1381 42 y(gr)n(amming)p @F18 @sf(,)g(R)o(UTCOR)g
(Researc)o(h)d(Rep)q(ort,)g(RRR)i(#4{92,)e(1992.)-976 41 y(11.)17 b(McGeo)q
(c)o(h,)o 10 x(C.)11 b(C.,)g @F3 @sf(The)h(First)g(DIMA)o(CS)f
(International)i(A)o(lgorithm)g(Implementation)g(Chal)r(lenge:)-1380 42 y
(The)g(Cor)n(e)g(Exp)n(eriments)p @F18 @sf(,)g(DIMA)o(CS,)f(August,)e
(1991.)-813 41 y(12.)17 b(McGeo)q(c)o(h,)o 10 x(C.)11 b(C.,)g @F3 @sf(The)h
(First)g(DIMA)o(CS)f(International)i(A)o(lgorithm)g(Implementation)g(Chal)r
(lenge:)-1380 42 y(The)g(Benchmark)h(Exp)n(erime)q(nts)p @F18 @sf(,)e
(DIMA)o(CS,)g(Decem)o(b)q(er,)e(1991.)-906 91 y @F1 @sf(Computer)j(and)g
(A)o(utoma)n(tion)f(Institute,)j(Hungarian)d(A)o(cademy)h(of)h(Sciences,)g
(H{1518)-1444 42 y(Bud)o(apest,)h(P.O.Bo)o(x)d(63.,)i(Hungar)n(y)-526 54 y 
@F3 @sf(Curr)n(ent)f(addr)n(ess)s @F18 @sf(:)k(R)o(UTCOR,)c(Rutgers)e(Cen)o
(ter)g(for)g(Op)q(erations)f(Researc)o(h,)o 11 x(Rutgers)h(Univ)o(ersit)o
(y)o -3 x(,)-1446 41 y(P)m(.O.Bo)o(x)g(5062,)f(New)j(Brunswic)o(k,)o 11 x
(NJ)f(08903)-590 54 y @F3 @sf(E-mail)h(addr)n(ess)s @F18 @sf(:)k
(maros@rutcor.r)o(utg)o(ers.)p(e)o(du)o 11 x(and)10 b(h107mar@ella)o(.h)o
(u)o -1050 303 a
19 @eop1

(\nEND-JOB maros.dvi\n) print flush
restore
