New deterministic approximation algorithms for fully dynamic matching

We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a (2+є)-approximate maximum matching in general graphs with O ( poly (log n , 1/є)) update time. (2) An algorithm that maintains an α K approximation of the value of the maximum matching with O ( n 2/ K ) update time in bipartite graphs, for every sufficiently large constant positive integer K . Here, 1≤ α K < 2 is a constant determined by the value of K . Result (1) is the first deterministic algorithm that can maintain an o (log n )-approximate maximum matching with polylogarithmic update time, improving the seminal result of Onak et al. [STOC 2010]. Its approximation guarantee almost matches the guarantee of the best randomized polylogarithmic update time algorithm [Baswana et al. FOCS 2011]. Result (2) achieves a better-than-two approximation with arbitrarily small polynomial update time on bipartite graphs. Previously the best update time for this problem was O ( m 1/4 ) [Bernstein et al. ICALP 2015], where m is the current number of edges in the graph.

Authors

• Sayan Bhattacharya
• Monika Henzinger
• Danupon Nanongkai

Keywords

• Data Structures
• Dynamic Graph Algorithms