R(QPS-Serena) and R(QPS-Serenade): Two Novel Augmenting-Path Based Algorithms for Computing Approximate Maximum Weight Matching
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In this addendum, we show that the switching algorithm QPS-SERENA can be converted R(QPS-SERENA), an algorithm for computing approximate Maximum Weight Matching (MWM). Empirically, R(QPS-SERENA) computes (1-ϵ)-MWM within linear time (with respect to the number of edges N^2) for any fixed ϵ∈ (0,1), for complete bipartite graphs with i.i.d. uniform edge weight distributions. This efficacy matches that of the state-of-art solution, although we so far cannot prove any theoretical guarantees on the time complexities needed to attain a certain approximation ratio. Then, we have similarly converted QPS-SERENADE to R(QPS-SERENADE), which empirically should output (1-ϵ)-MWM within only O(N N) time for the same type of complete bipartite graphs as described above.
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