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- W2136742671 abstract "Randomized algorithms for approximating the number of perfect matchings in a graph are considered. An algorithm that is a natural simplification of one suggested and analyzed previously is introduced and analyzed. One of the key ideas is to view the analysis from a geometric perspective: it is proved that for any graph G the k-slice of the well-known Edmonds matching polytope has magnification 1. For a bipartite graph G=(U, V, E), mod U mod = mod V mod =n, with d edge-disjoint perfect matchings, it is proved that the ratio of the number of almost perfect matchings to the number of perfect matchings is at most n/sup 3n/d/. For any constant alpha >0 this yields a a fully polynomial randomized algorithm for approximating the number of perfect matchings in bipartite graphs with d>or= alpha n. Moreover, for some constant c>0 it is the fastest known approximation algorithm for bipartite graphs with d>or= clog n.< <ETX xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>></ETX>" @default.
- W2136742671 created "2016-06-24" @default.
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- W2136742671 date "1988-01-01" @default.
- W2136742671 modified "2023-10-06" @default.
- W2136742671 title "Polytopes, permanents and graphs with large factors" @default.
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- W2136742671 doi "https://doi.org/10.1109/sfcs.1988.21957" @default.
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