Consider a two-stage matching problem, where edges of an input graph are revealed in two stages (batches) and in each stage we have to immediately and irrevocably extend our matching using the edges from that stage. The natural greedy algorithm is half ...

Given a weighted planar bipartite graph G(A ∪ B, E) where each edge has an integer edge cost, we give an Õ(n^4/3log nC) time algorithm to compute minimum-cost perfect matching; here C is the maximum edge cost in the graph. The previous best-known ...

Recently, hardness results for problems in P were achieved using reasonable complexity-theoretic assumptions such as the Strong Exponential Time Hypothesis. According to these assumptions, many graph-theoretic problems do not admit truly subquadratic ...

We present a simple deterministic single-pass (2+ϵ)-approximation algorithm for the maximum weight matching problem in the semi-streaming model. This improves on the currently best known approximation ratio of (4+ϵ).

Our algorithm uses O(nlog² n) bits ...

We consider the problem of estimating the size of a maximum matching when the edges are revealed in a streaming fashion. When the input graph is planar, we present a simple and elegant streaming algorithm that, with high probability, estimates the size ...

We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in O(m√nlog(nN)) time, O(m√ n) per scale, which matches the running time of the best cardinality matching algorithms ...