TL;DR
This paper introduces the first deterministic algorithms that outperform the folklore approach for dynamic graph matching, achieving better approximation ratios and worst-case update times in both unweighted and weighted cases.
Contribution
It presents new deterministic algorithms for dynamic matching that surpass the folklore algorithm in approximation ratio and update time, including characterizations of kernels and improved recourse techniques.
Findings
Achieved a (2−Ω(1))-approximate algorithm with O(n^{3/4}) update time.
Developed a (2+ε)-approximate weighted matching algorithm with O(√n) update time.
Characterized tight cases for kernels, enhancing understanding of approximation barriers.
Abstract
The maximum matching problem in dynamic graphs subject to edge updates (insertions and deletions) has received much attention over the last few years; a multitude of approximation/time tradeoffs were obtained, improving upon the folklore algorithm, which maintains a maximal (and hence -approximate) matching in worst-case update time in -node graphs. We present the first deterministic algorithm which outperforms the folklore algorithm in terms of {\em both} approximation ratio and worst-case update time. Specifically, we give a -approximate algorithm with worst-case update time in -node, -edge graphs. For sufficiently small constant , no deterministic -approximate algorithm with worst-case update time was known. Our second result is the first deterministic -approximate…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
Beating the Folklore Algorithm for Dynamic Matching· youtube
