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Title: Dynamic Matching with Better-than-2 Approximation in Polylogarithmic Update Time

We present dynamic algorithms withpolylogarithmicupdate time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratiostrictly better than 2. Specifically, we obtain a\(1+\frac{1}{\sqrt {2}}+\epsilon \approx 1.707+\epsilon \)approximation in bipartite graphs and a 1.973 + ϵ approximation in general graphs. We thus answer in the affirmative the value version of the major open question repeatedly asked in the dynamic graph algorithms literature. Our randomized algorithms’ approximation and worst-case update time bounds both hold w.h.p. against adaptive adversaries.

Our algorithms are based on simulating new two-pass streaming matching algorithms in the dynamic setting. Our key new idea is to invoke the recent sublinear-time matching algorithm of Behnezhad (FOCS’21) in a white-box manner to efficiently simulate the second pass of our streaming algorithms, while bypassing the well-known vertex-update barrier.

 
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Award ID(s):
2238138
PAR ID:
10536452
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Association for Computing Machinery
Date Published:
Journal Name:
Journal of the ACM
ISSN:
0004-5411
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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