
\newcommand{\rar}[2]{{{\em #1}\(\rightarrow\){\em #2}}}
\newcommand{\Container}{{\em Container}}
\newcommand{\ContainerNode}{{\em ContainerNode}}
\newcommand{\ElementOps}{{\em ElementOps}}
\newcommand{\FlowInfo}{{\em FlowInfo}}
\newcommand{\Array}{{\em Array}}
\newcommand{\SortedArray}{{\em SortedArray}}
\newcommand{\SortedList}{{\em SortedList}}
\newcommand{\List}{{\em List}}
\newcommand{\Item}{{\em Item}}
\newcommand{\ListNode}{{\em ListNode}}
\newcommand{\Queue}{{\em Queue}}
\newcommand{\Deque}{{\em Deque}}
\newcommand{\Stack}{{\em Stack}}
\newcommand{\DList}{{\em DList}}
\newcommand{\Permutation}{{\em Permutation}}
\newcommand{\Matrix}{{\em Matrix}}
\newcommand{\BinaryHeap}{{\em BinaryHeap}}
\newcommand{\BinaryHeapNode}{{\em BinaryHeapNode}}
\newcommand{\BinarySearchTree}{{\em BinarySearchTree}}
\newcommand{\RedBlackTree}{{\em RedBlackTree}}
\newcommand{\BinomialHeap}{{\em BinomialHeap}}
\newcommand{\SimpleContainer}{{\em SimpleContainer}}
\newcommand{\Dictionary}{{\em Dictionary}}
\newcommand{\Collection}{{\em Collection}}
\newcommand{\SetBase}{{\em SetBase}}
\newcommand{\MSetBase}{{\em MSetBase}}
\newcommand{\SymSet}{{\em SymSet}}
\newcommand{\Set}{{\em Set}}
\newcommand{\MSet}{{\em MSet}}
\newcommand{\SubSet}{{\em SubSet}}
\newcommand{\SequenceBase}{{\em SequenceBase}}
\newcommand{\Sequence}{{\em Sequence}}
\newcommand{\Iterator}{{\em Iterator}}
\newcommand{\GraphObject}{{\em GraphObject}}
\newcommand{\Graph}{{\em Graph}}
\newcommand{\Subgraph}{{\em Subgraph}}
\newcommand{\MUHyperGraph}{{\em MUHyperGraph}}
\newcommand{\MDHyperGraph}{{\em MDHyperGraph}}
\newcommand{\MBinGraph}{{\em MBinGraph}}
\newcommand{\MUBinGraph}{{\em MUBinGraph}}
\newcommand{\MDBinGraph}{{\em MDBinGraph}}
\newcommand{\HyperGraph}{{\em HyperGraph}}
\newcommand{\UHyperGraph}{{\em UHyperGraph}}
\newcommand{\DHyperGraph}{{\em DHyperGraph}}
\newcommand{\BinGraph}{{\em BinGraph}}
\newcommand{\UBinGraph}{{\em UBinGraph}}
\newcommand{\DBinGraph}{{\em DBinGraph}}
\newcommand{\Vertex}{{\em Vertex}}
\newcommand{\Edge}{{\em Edge}}
\newcommand{\Attribute}{{\em Attribute}}
\newcommand{\GraphView}{{\em GraphView}}
\newcommand{\Graphic}{{\em Graphic}}
\newcommand{\VertexGraphic}{{\em VertexGraphic}}
\newcommand{\EdgeGraphic}{{\em EdgeGraphic}}
\newcommand{\Graphics}{{\em Graphics}}
\newcommand{\GraphWindow}{{\em GraphWindow}}
\newcommand{\GraphCanvas}{{\em GraphCanvas}}
\newcommand{\Canvas}{{\em Canvas}}
\newcommand{\GraphShell}{{\em GraphShell}}
\newcommand{\Selection}{{\em Selection}}

\newcommand{\Containers}{{\em Containers}}
\newcommand{\ContainerNodes}{{\em ContainerNodes}}
\newcommand{\Arrays}{{\em Arrays}}
\newcommand{\SortedArrays}{{\em SortedArrays}}
\newcommand{\SortedLists}{{\em SortedLists}}
\newcommand{\Lists}{{\em Lists}}
\newcommand{\Items}{{\em Items}}
\newcommand{\ListNodes}{{\em ListNodes}}
\newcommand{\Queues}{{\em Queues}}
\newcommand{\Deques}{{\em Deques}}
\newcommand{\Stacks}{{\em Stacks}}
\newcommand{\DLists}{{\em DLists}}
\newcommand{\Matrices}{{\em Matrices}}
\newcommand{\Permutations}{{\em Permutations}}
\newcommand{\BinaryHeaps}{{\em BinaryHeaps}}
\newcommand{\BinaryHeapNodes}{{\em BinaryHeapNodes}}
\newcommand{\BinarySearchTrees}{{\em BinarySearchTrees}}
\newcommand{\RedBlackTrees}{{\em RedBlackTrees}}
\newcommand{\BinomialHeaps}{{\em BinomialHeaps}}
\newcommand{\SimpleContainers}{{\em SimpleContainers}}
\newcommand{\Collections}{{\em Collections}}
\newcommand{\SetBases}{{\em SetBases}}
\newcommand{\MSetBases}{{\em MSetBases}}
\newcommand{\SymSets}{{\em SymSets}}
\newcommand{\Sets}{{\em Sets}}
\newcommand{\MSets}{{\em MSets}}
\newcommand{\SubSets}{{\em SubSets}}
\newcommand{\SequenceBases}{{\em SequenceBases}}
\newcommand{\Sequences}{{\em Sequences}}
\newcommand{\Iterators}{{\em Iterators}}
\newcommand{\VertexGraphics}{{\em VertexGraphics}}
\newcommand{\EdgeGraphics}{{\em EdgeGraphics}}
\newcommand{\GraphObjects}{{\em GraphObjects}}
\newcommand{\Graphs}{{\em Graphs}}
\newcommand{\Subgraphs}{{\em Subgraphs}}
\newcommand{\MUHyperGraphs}{{\em MUHyperGraphs}}
\newcommand{\MDHyperGraphs}{{\em MDHyperGraphs}}
\newcommand{\MBinGraphs}{{\em MBinGraphs}}
\newcommand{\MUBinGraphs}{{\em MUBinGraphs}}
\newcommand{\MDBinGraphs}{{\em MDBinGraphs}}
\newcommand{\HyperGraphs}{{\em HyperGraphs}}
\newcommand{\UHyperGraphs}{{\em UHyperGraphs}}
\newcommand{\DHyperGraphs}{{\em DHyperGraphs}}
\newcommand{\BinGraphs}{{\em BinGraphs}}
\newcommand{\UBinGraphs}{{\em UBinGraphs}}
\newcommand{\DBinGraphs}{{\em DBinGraphs}}
\newcommand{\Vertices}{{\em Vertices}}
\newcommand{\Edges}{{\em Edges}}
\newcommand{\Attributes}{{\em Attributes}}
\newcommand{\GraphViews}{{\em GraphViews}}
\newcommand{\GraphWindows}{{\em GraphWindows}}
\newcommand{\Selections}{{\em Selections}}

%with a padding space afterwards

\newcommand{\MHyperGraph}{{\em MHyperGraph}\ }
\newcommand{\MHyperGraphs}{{\em MHyperGraphs}\ }

\newcommand{\MHyperGraphn}{{\em MHyperGraph}}
\newcommand{\MHyperGraphsn}{{\em MHyperGraphs}}

\newcommand{\SetFuncs}{{\em{SetFuncs}}\ }
\newcommand{\SetFuncsn}{{\em{SetFuncs}}}

\newcommand{\ronei}{{\mbox{$r_1(i)$}}}
\newcommand{\rji}{{\mbox{$r_j(i)$}}}

\newcommand{\lowerb}{{\em lower\_bound}\ }
\newcommand{\lowerbn}{{\em lower\_bound}}

\newcommand{\upperb}{{\em upper\_bound}\ }
\newcommand{\upperbn}{{\em upper\_bound}}

\newcommand{\type}{{\em type}\ }
\newcommand{\typen}{{\em type}}

\newcommand{\vlist}{{\em vlist}\ }
\newcommand{\vlistn}{{\em vlist}}

\newcommand{\elist}{{\em elist}\ }
\newcommand{\elistn}{{\em elist}}

\newcommand{\integer}{{\em integer}\ }
\newcommand{\integern}{{\em integer}}

\newcommand{\kn} {{$k_n$}}

\newcommand{\emsymbol}{{\em symbol}\ }
\newcommand{\emsymboln}{{\em symbol}}

\newcommand{\emlist}{{\em list}\ }
\newcommand{\emlistn}{{\em list}}

\newcommand{\emlistone}{\mbox{$l_1$}\ }
\newcommand{\emlistonen}{\mbox{$l_1$}}

\newcommand{\emlisttwo}{\mbox{$l_2$}\ }
\newcommand{\emlisttwon}{\mbox{$l_2$}}

\newcommand{\emlistk}{\mbox{$l_k$}\ }
\newcommand{\emlistkn}{\mbox{$l_k$}}

\newcommand{\emlisti}{\mbox{$l_i$}\ }
\newcommand{\emlistin}{\mbox{$l_i$}}

\newcommand{\emlistj}{\mbox{$l_j$}\ }
\newcommand{\emlistjn}{\mbox{$l_j$}}

\newcommand{\vect}{\mbox{$vec$}\ }
\newcommand{\vectn}{\mbox{$vec$}}

\newcommand{\vectone}{\mbox{$vec_1$}\ }
\newcommand{\vectonen}{\mbox{$vec_1$}}

\newcommand{\vecttwo}{\mbox{$vec_2$}\ }
\newcommand{\vecttwon}{\mbox{$vec_2$}}

\newcommand{\vectk}{\mbox{$vec_k$}\ }
\newcommand{\vectkn}{\mbox{$vec_k$}}

\newcommand{\vecti}{\mbox{$vec_i$}\ }
\newcommand{\vectin}{\mbox{$vec_i$}}

\newcommand{\vectj}{\mbox{$vec_j$}\ }
\newcommand{\vectjn}{\mbox{$vec_j$}}

\newcommand{\collection}{\mbox{$collection$}\ }
\newcommand{\collectionn}{\mbox{$collection$}}

\newcommand{\col}{\mbox{$col$}\ }
\newcommand{\coln}{\mbox{$col$}}

\newcommand{\colone}{\mbox{$col$}\ }
\newcommand{\colonen}{\mbox{$col$}}

\newcommand{\coltwo}{\mbox{$col_2$}\ }
\newcommand{\coltwon}{\mbox{$col_2$}}

\newcommand{\colk}{\mbox{$col_k$}\ }
\newcommand{\colkn}{\mbox{$col_k$}}

\newcommand{\coli}{\mbox{$col_i$}\ }
\newcommand{\colin}{\mbox{$col_i$}}

\newcommand{\colj}{\mbox{$col_j$}\ }
\newcommand{\coljn}{\mbox{$col_j$}}

\newcommand{\set}{\mbox{$set$}\ }
\newcommand{\setn}{\mbox{$set$}}

\newcommand{\setone}{\mbox{$set$}\ }
\newcommand{\setonen}{\mbox{$set$}}

\newcommand{\settwo}{\mbox{$set_2$}\ }
\newcommand{\settwon}{\mbox{$set_2$}}

\newcommand{\setk}{\mbox{$set_k$}\ }
\newcommand{\setkn}{\mbox{$set_k$}}

\newcommand{\seti}{\mbox{$set_i$}\ }
\newcommand{\setin}{\mbox{$set_i$}}

\newcommand{\setj}{\mbox{$set_j$}\ }
\newcommand{\setjn}{\mbox{$set_j$}}

\newcommand{\sequence}{\mbox{$sequence$}\ }
\newcommand{\sequencen}{\mbox{$sequence$}}

\newcommand{\sequenceone}{\mbox{$sequence$}\ }
\newcommand{\sequenceonen}{\mbox{$sequence$}}

\newcommand{\sequencetwo}{\mbox{$sequence_2$}\ }
\newcommand{\sequencetwon}{\mbox{$sequence_2$}}

\newcommand{\sequencek}{\mbox{$sequence_k$}\ }
\newcommand{\sequencekn}{\mbox{$sequence_k$}}

\newcommand{\sequencei}{\mbox{$sequence_i$}\ }
\newcommand{\sequencein}{\mbox{$sequence_i$}}

\newcommand{\sequencej}{\mbox{$sequence_j$}\ }
\newcommand{\sequencejn}{\mbox{$sequence_j$}}

\newcommand{\ms}{{\em ms}\ }
\newcommand{\msn}{{\em ms}}

\newcommand{\setvertex}{\mbox{$set-vertex$}\ }
\newcommand{\setvertexn}{\mbox{$set-vertex$}}

\newcommand{\msetvertex}{\mbox{$mset-vertex$}\ }
\newcommand{\msetvertexn}{\mbox{$mset-vertex$}}

\newcommand{\setedge}{\mbox{$set-edge$}\ }
\newcommand{\setedgen}{\mbox{$set-edge$}}

\newcommand{\msetedge}{\mbox{$mset-edge$}\ }
\newcommand{\msetedgen}{\mbox{$mset-edge$}}

\newcommand{\mset}{\mbox{$mset$}\ }
\newcommand{\msetn}{\mbox{$mset$}}

\newcommand{\msetone}{\mbox{$mset$}\ }
\newcommand{\msetonen}{\mbox{$mset$}}

\newcommand{\msettwo}{\mbox{$mset_2$}\ }
\newcommand{\msettwon}{\mbox{$mset_2$}}

\newcommand{\msetk}{\mbox{$mset_k$}\ }
\newcommand{\msetkn}{\mbox{$mset_k$}}

\newcommand{\mseti}{\mbox{$mset_i$}\ }
\newcommand{\msetin}{\mbox{$mset_i$}}

\newcommand{\msetj}{\mbox{$mset_j$}\ }
\newcommand{\msetjn}{\mbox{$mset_j$}}

\newcommand{\g} {\mbox{$g$}\  }
\newcommand{\gn}{\mbox{$g$}}

\newcommand{\gv} {\mbox{$gv$}\  }
\newcommand{\gvn}{\mbox{$gv$}}

\newcommand{\vg} {\mbox{$vg$}\  }
\newcommand{\vgn}{\mbox{$vg$}}

\newcommand{\eg} {\mbox{$eg$}\  }
\newcommand{\egn}{\mbox{$eg$}}

\newcommand{\graph} {\mbox{$graph$}\ }
\newcommand{\graphn}{\mbox{$graph$}  }

\newcommand{\graphone} {\mbox{$graph$}\ }
\newcommand{\graphonen}{\mbox{$graph$}  }

\newcommand{\graphtwo}{\mbox{$graph_2$}\ }
\newcommand{\graphtwon}{\mbox{$graph_2$}  }

\newcommand{\graphk}{\mbox{$graph_k$}\ }
\newcommand{\graphkn}{\mbox{$graph_k$}  }

\newcommand{\graphi}{\mbox{$graph_i$}\ }
\newcommand{\graphin}{\mbox{$graph_i$}  }

\newcommand{\graphj}{\mbox{$graph_j$}\ }
\newcommand{\graphjn}{\mbox{$graph_j$}  }

\newcommand{\vi} {\mbox{$vi$}\ }
\newcommand{\vin}{\mbox{$vi$}  }

\newcommand{\vertex}{\mbox{$vertex$}\ }
\newcommand{\vertexn}{\mbox{$vertex$}}

\newcommand{\vertexone}{\mbox{$vertex$}\ }
\newcommand{\vertexonen}{\mbox{$vertex$}  }

\newcommand{\vertextwo}{\mbox{$vertex_2$}\ }
\newcommand{\vertextwon}{\mbox{$vertex_2$}  }

\newcommand{\vertexk}{\mbox{$vertex_k$}\ }
\newcommand{\vertexkn}{\mbox{$vertex_k$}  }

\newcommand{\vertexi}{\mbox{$vertex_i$}\ }
\newcommand{\vertexin}{\mbox{$vertex_i$}  }

\newcommand{\vertexj}{\mbox{$vertex_j$}\ }
\newcommand{\vertexjn}{\mbox{$vertex_j$}  }

\newcommand{\ei}{\mbox{$ei$}\ }
\newcommand{\ein}{\mbox{$ei$}}

\newcommand{\edge}{\mbox{$edge$}\ }
\newcommand{\edgen}{\mbox{$edge$}}

\newcommand{\edgeone}{\mbox{$edge$}\ }
\newcommand{\edgeonen}{\mbox{$edge$}}

\newcommand{\edgetwo}{\mbox{$edge_2$}\ }
\newcommand{\edgetwon}{\mbox{$edge_2$}}

\newcommand{\edgek}{\mbox{$edge_k$}\ }
\newcommand{\edgekn}{\mbox{$edge_k$}}

\newcommand{\edgei}{\mbox{$edge_i$}\ }
\newcommand{\edgein}{\mbox{$edge_i$}}

\newcommand{\edgej}{\mbox{$edge_j$}\ }
\newcommand{\edgejn}{\mbox{$edge_j$}}

\newcommand{\val}{{\em value}\ }
\newcommand{\valn}{{\em value}}

\newcommand{\ind}{{\em index}\ }
\newcommand{\indn}{{\em index}}

\newcommand{\newsize}{{\em newsize}\ }
\newcommand{\newsizen}{{\em newsize}}

\newcommand{\size}{{\em size}\ }
\newcommand{\sizen}{{\em size}}

\newcommand{\ione}{\mbox{$i_1$}\ }
\newcommand{\ionen}{\mbox{$i_1$}}

\newcommand{\itwo}{\mbox{$i_2$}\ }
\newcommand{\itwon}{\mbox{$i_2$}}

\newcommand{\ithree}{\mbox{$i_3$}\ }
\newcommand{\ithreen}{\mbox{$i_3$}}

\newcommand{\ik}{\mbox{$i_k$}\ }
\newcommand{\ikn}{\mbox{$i_k$}}

\newcommand{\lth}{\mbox{$<$}\ }
\newcommand{\lthn}{\mbox{$<$}}

\newcommand{\ltheq}{\mbox{$<=$}\ }
\newcommand{\ltheqn}{\mbox{$<=$}}

\newcommand{\gth}{\mbox{$>$}\ }
\newcommand{\gthn}{\mbox{$>$}}

\newcommand{\gtheq}{\mbox{$>=$}\ }
\newcommand{\gtheqn}{\mbox{$>=$}}

\newcommand{\equal}{\mbox{$==$}\ }
\newcommand{\equaln}{\mbox{$==$}}

\newcommand{\notequal}{\mbox{$!=$}\ }
\newcommand{\notequaln}{\mbox{$!=$}}

\newcommand{\xpixels}{{\em xpixels}\ }
\newcommand{\xpixelsn}{{\em xpixels}}

\newcommand{\ypixels}{{\em ypixels}\ }
\newcommand{\ypixelsn}{{\em ypixels}}

\newcommand{\name}{{\em name}\ }
\newcommand{\namen}{{\em name}}

\newcommand{\layout}{{\em layout}\ }
\newcommand{\layoutn}{{\em layout}}

\newcommand{\creation}{
\noindent{\bf 1. Creation}

\vspace{0.3in}
}

\newcommand{\operations}{
\noindent{\bf 2. Operations}

\vspace{0.3in}
}

\newcommand{\implementations}{
\noindent{\bf 3. Implementations}

\vspace{0.3in}
}

\newcommand{\utilities}{
\noindent{\bf 3. Utilities}

\vspace{0.3in}
}
\renewcommand{\thefigure}{\thesection.\arabic{figure}}
\renewcommand{\topfraction} {0.9}
\renewcommand{\bottomfraction} {0.9}

