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)


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).


Approximation Algorithm Edge Weight Basic Interval Maximum Weight Match Bound Degree Graph 
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© 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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