Digraphs+Theory,+Algorithms+and+Applications_Part39

Digraphs+Theory,+Algorithms+and+Applications_Part39 -...

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Unformatted text preview: Subject Index 743 relation to chromatic number, 433 longest path problem, 195 acyclic digraph, 89 weighted acyclic digraph, 53 loop, 4 Lov´ asz’s local lemma, 569 Lov´ asz’s splitting theorem, 440, 468 lower bound on an arc, 95 removing from a network, 99 Lucchesi-Younger theorem, 399 proof using submodular flows, 457 Mader’s directed splitting theorem, 358 main ( n 1 ,...,n p )-blocks, 221 majority digraph of a hypertourna- ment, 628 Marcus’ theorem, 581 Markov chain, 563 matching, 22, 442 perfect, 22 matching diagram digraph, 217 matrix multiplication, 177 matroid, 525, 663–671 base, 663 circuit, 663 cocircuit, 666 cutset, 666 dependent set, 663 dual, 665 examples of, 664 fast algorithm, 667 greedy algorithm, 666, 678 greedy base, 666 independence oracle, 667 independent set, 663 intersection, 669 optimal base, 666 rank, 664 union, 668 matroid intersection, 457 matroid intersection problem, 525, 669, 679 k-matroid intersection problem, 670 matroid partition problem, 668, 678 MAX-2-SAT, 38, 44 Max-flow Min-cut theorem, 109 application to vertex cover in bi- partite graphs, 139 relation to Menger’s theorem, 351 1-maximal cycle, 44 maximal flow, 112 maximal hamiltonian arc-critical subdigraph, 432 maximal independent subset of a set in a matroid, 664 maximal with respect to property P , 2 maximum adjacency ordering, 355 determining edge-connectivity via, 356 maximum capacity augmenting path method, 164 maximum finite diameter orientation, 61 maximum flow algorithms, 110–125 capacity scaling algorithm, 162 Dinic’s algorithm, 116 for unit capacity networks, 123 Ford-Fulkerson algorithm, 110 maximum capacity augmenting path method, 164 MKM algorithm, 161 on simple networks, 125 preflow push algorithm, 119 shortest augmenting paths, 114 maximum flow problem, 108–125 and arc-strong connectivity, 353 in unit capacity networks, 123 integrality theorem, 112 re-optimizing after small pertur- bation, 161 maximum in-degree of a digraph, 5 maximum matching in bipartite graphs, 137 algorithm, 138 reduction to flow problem, 137 maximum monochromatic degree, 591 maximum out-degree of a digraph, 5 maximum semi-degree of a digraph, 5 maximum with respect to property P , 2 mean cost of a cycle, 134 median order, 638 member of a family of digraphs, 7 member of a family of sets, 344 Menger’s theorem, 147, 293, 297, 351–354, 356, 360, 365, 372, 374, 384, 396, 408, 409, 441, 442, 456, 474, 499–501, 517, 518, 537, 538, 586 applied to sets of vertices, 408 744 Subject Index refinement of, 408 relation to the Max-flow Min- cut theorem, 408 Mergesort, 32 merging paths in a digraph, see path- mergaeble digraph meta-heuristic, 673 Meyniel set, 243 Min-flow Max-demand theorem, 127 minimal ( x,y )-path, 11 minimal vertex series-parallel di- graphs, 191 minimally k-arc-strong directed multigraph, 379–384 characterization of, 384 degree of vertices in, 381 number of arcs in, 380 minimally k-edge-connected multi- graph, 441, 468 minimally k-strong digraph, 384–388...
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