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The Holt-Klee Condition states that there exist at least d vertex-disjoint strictly monotone paths from the source to the sink of a polytopal digraph consisting of the set of vertices
and arcs of a polytope P directed by a linear objective function in general position. The study of paths on polytopal digraphs stems from a long standing
problem, that of designing a polynomial-time pivot method, or proving none exists. To study disjoint paths it would be useful
to have a tool to compute them. Without explicitly computing the digraph we develop an algorithm to compute a maximum cardinality
set of source to sink paths in a polytope, even in the presence of degeneracy. The algorithm uses a combination of networks
flows, the simplex method, and reverse search. An implementation is available. 相似文献
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Bohdan Harasymiw 《Canadian Slavonic papers》2013,55(2-3):160-181
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