Multiplicative auction algorithm for approximate maximum weight bipartite matching

We present an auction algorithm using multiplicative instead of constant weight updates to compute a (1-ε ) -approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time O(mε ^-1) , beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in O(mε ^-1logε ^-1) . Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a (1-ε ) -approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time time used is O(mε ^-1) , where m is the sum of the number of initially existing and inserted edges.