Maintaining Approximate Maximum Matching in an Incremental Bipartite Graph in Polylogarithmic Update Time
نویسنده
چکیده
A sparse subgraph G′ of G is called a matching sparsifier if the size or weight of matching in G′ 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 + ) approximate matching in an incremental bipartite graph in O( log 2 n 4 ) update time. 2. For weighted graphs, we design an algorithm that maintains (1 + ) approximate weighted matching in O( logn log(nN) 4 ) update time where N is the maximum weight of any edge in the graph. 1998 ACM Subject Classification E.1 [Data Structures]: Graphs and Networks, F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems, G.2.2 [Graph Theory]: Graph Algorithms
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