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-E)-approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time 0(mE-1), beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in 0(mE-1 log E-1). Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a (1-E)-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 0(mE-1), where m is the sum of the number of initially existing and inserted edges.