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arXiv · 1207.3976

Maintaining Approximate Maximum Weighted Matching in Fully Dynamic Graphs

Abhash Anand·Surender Baswana·Manoj Gupta·Sandeep Sen
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Abstract

We present a fully dynamic algorithm for maintaining approximate maximum weight matching in general weighted graphs. The algorithm maintains a matching ${\cal M}$ whose weight is at least $1/8 M^{*}$ where $M^{*}$ is the weight of the maximum weight matching. The algorithm achieves an expected amortized $O(\log n \log \mathcal C)$ time per edge insertion or deletion, where $\mathcal C$ is the ratio of the weights of the highest weight edge to the smallest weight edge in the given graph. Using a simple randomized scaling technique, we are able to obtain a matching whith expected approximation ratio 4.9108.

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Abhash Anand, Surender Baswana, Manoj Gupta, Sandeep Sen. 2012-12-12. Maintaining Approximate Maximum Weighted Matching in Fully Dynamic Graphs. https://arxiv.org/abs/1207.3976

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