Near Approximation of Maximum Weight Matching through Efficient Weight Reduction
نویسندگان
چکیده
Let G be an edge-weighted hypergraph on n vertices, m edges of size O(1), 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 − ǫ) times the maximum weight of a matching in G in time (ǫ) max 1≤q≤O(ǫ log n ǫ log ǫ−1 ) maxm1+...mq=m ∑q 1 T (n,mj , (ǫ ) −1)). In particular, if we combine our result with the recent (1 − ǫ)-approximation algorithm for maximum weight matching in graphs with small edge weights due to Duan and Pettie then we obtain (1 − ǫ)-approximation algorithm for maximum weight matching in graphs running in time (ǫ) −1)(m+ n log n).
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