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arXiv · 1810.01073

Fully dynamic $3/2$ approximate maximum cardinality matching in $O(\sqrt{n})$ update time

Manas Jyoti Kashyop·N. S. Narayanaswamy
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Abstract

We present a randomized algorithm to maintain a maximal matching without 3 length augmenting paths in the fully dynamic setting. Consequently, we maintain a $3/2$ approximate maximum cardinality matching. Our algorithm takes expected amortized $O(\sqrt{n})$ time where $n$ is the number of vertices in the graph when the update sequence is generated by an oblivious adversary. Over any sequence of $t$ edge insertions and deletions presented by an oblivious adversary, the total update time of our algorithm is $O(t\sqrt{n})$ in expectation and $O(t\sqrt{n} + n \log n)$ with high probability. To the best of our knowledge, our algorithm is the first one to maintain an approximate matching in which all augmenting paths are of length at least $5$ in $o(\sqrt{m})$ update time.

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Manas Jyoti Kashyop, N. S. Narayanaswamy. 2018-10-02. Fully dynamic $3/2$ approximate maximum cardinality matching in $O(\sqrt{n})$ update time. https://arxiv.org/abs/1810.01073

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