LIPIcs - Leibniz International Proceedings in Informatics. 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Doi
Abstract
A sparse subgraph G\u27 of G is called a matching sparsifier if the size or weight of matching in G\u27 is approximately equal to the size or weight of maximum matching in G. Recently, algorithms have been developed to find matching sparsifiers in a static bipartite graph. In this paper, we show that we can find matching sparsifier even in an incremental bipartite graph.
This observation leads to following results: 1. We design an algorithm that maintains a (1+epsilon) approximate matching in an incremental bipartite graph in O(log^2(n) / (epsilon^{4}) update time. 2. For weighted graphs, we design an algorithm that maintains (1+epsilon) approximate weighted matching in O((log(n)*log(n*N)) / (epsilon^4) update time where maxweight is the maximum weight of any edge in the graph
