Rounding dynamic matchings against an adaptive adversary

We present a new dynamic matching sparsification scheme. From this scheme we derive a framework for dynamically rounding fractional matchings against adaptive adversaries. Plugging in known dynamic fractional matching algorithms into our framework, we obtain numerous randomized dynamic matching algorithms which work against adaptive adversaries. In contrast, all previous randomized algorithms for this problem assumed a weaker, oblivious, adversary. Our dynamic algorithms against adaptive adversaries include, for any constant є >0, a (2+є)-approximate algorithm with constant update time or polylog worst-case update time, as well as (2−δ)-approximate algorithms in bipartite graphs with arbitrarily-small polynomial update time. All these results achieve polynomially better update time to approximation trade-offs than previously known to be achievable against adaptive adversaries.