Near approximation of maximum weight matching through efficient weight reduction

  • Authors:

  • Andrzej Lingas;Cui Di

  • Affiliations:

  • Department of Computer Science, Lund University, Lund, Sweden;Department of Computer Science, Lund University, Lund, Sweden

  • Venue:
  • TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
  • Year:
  • 2011

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Abstract

Let G be an edge-weighted hypergraph on n vertices, m edges of size ≤ 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 α in time T(n, m, W) then we can find a matching of weight at least (α - ε) times the maximum weight of a matching in G in time (ε-1)O(1)× max1≤q≤O(ε log n/ε/log ε-1) maxm1+...mq=m Σ1qT(min{n, smj},mj, (ε-1)O(ε-1)). We obtain our result by an approximate reduction of the original problem to O(ε logn/ε/log ε-1) subproblems with edge weights bounded by (ε-1)O(ε-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 (ε-1)O(1)(m+n).