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arXiv · 1012.5911

Near approximation of maximum weight matching through efficient weight reduction

Andrzej Lingas·Cui Di
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Abstract

Let G be an edge-weighted hypergraph on n vertices, m edges of size \le s, where the edges have real weights in an interval [1,W]. We show that if we can approximate a maximum weight matching in G within factor alpha in time T(n,m,W) then we can find a matching of weight at least (alpha-epsilon) times the maximum weight of a matching in G in time (epsilon^{-1})^{O(1)}max_{1\le q \le O(epsilon \frac {log {\frac n {epsilon}}} {log epsilon^{-1}})} max_{m_1+...m_q=m} sum_1^qT(min{n,sm_j},m_{j},(epsilon^{-1})^{O(epsilon^{-1})}). In particular, if we combine our result with the recent (1-ε)-approximation algorithm for maximum weight matching in graphs due to Duan and Pettie whose time complexity has a poly-logarithmic dependence on W then we obtain a (1-ε)-approximation algorithm for maximum weight matching in graphs running in time (epsilon^{-1})^{O(1)}(m+n).

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Andrzej Lingas, Cui Di. 2011-01-11. Near approximation of maximum weight matching through efficient weight reduction. https://arxiv.org/abs/1012.5911

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