Near Approximation of Maximum Weight Matching through Efficient Weight Reduction

  • Andrzej Lingas
  • Cui Di
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6648)

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)× \(\max_{1\le q \le O(\epsilon \frac {\log {\frac n {\epsilon}}} {\log \epsilon^{-1}})} \max_{m_1+...m_q=m}\sum_1^qT(\min\{n,sm_j\},m_{j},(\epsilon^{-1})^{O(\epsilon^{-1})}).\) We obtain our result by an approximate reduction of the original problem to \(O(\epsilon \frac {\log {\frac n {\epsilon}}} {\log \epsilon^{-1}})\) subproblems with edge weights bounded by \((\epsilon^{-1})^{O(\epsilon^{-1})}.\) 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 (ε − 1) O(1)(m + n).

Keywords

Approximation Algorithm Edge Weight Basic Interval Maximum Weight Match Bound Degree Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andrzej Lingas
    • 1
  • Cui Di
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden

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