Fully Dynamic Matching in Bipartite Graphs

We present two fully dynamic algorithms for maximum cardinality matching in bipartite graphs. Our main result is a deterministic algorithm that maintains a (3/2 + epsilon) approximation in worst- case update time O(m(1/4) epsilon(-2.5)). This algorithm is polynomially faster than all previous deterministic algorithms for any constant approximation, and faster than all previous algorithms (randomized included) that achieve a better-than-2 approximation. We also give stronger results for bipartite graphs whose arboricity is at most a, achieving a (1 + epsilon) approximation in worst- case update time O(alpha(alpha + log(n)) + epsilon(-4) (alpha + log(n))+ epsilon(-6)), which is O(alpha(alpha + log n)) for constant epsilon. Previous results for small arboricity graphs had similar update times but could only maintain a maximal matching (2-approximation). All these previous algorithms, however, were not limited to bipartite graphs.