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+ ) approximation in worst-case update time O(m −2.5), which 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 α, achieving a (1 + ) approximation in worst-case update time O(α(α+logn)) for constant . 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.