Fully dynamic 3/2 approximate maximum cardinality matching in O(√(n)) update time
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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(√(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√(n)) in expectation and O(t√(n) + n 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(√(m)) update time.
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