eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-07-02
19:1
19:13
10.4230/LIPIcs.ICALP.2021.19
article
Beating Two-Thirds For Random-Order Streaming Matching
Assadi, Sepehr
1
Behnezhad, Soheil
2
Department of Computer Science, Rutgers University, Piscataway, NJ, USA
Department of Computer Science, University of Maryland, College Park, MD, USA
We study the maximum matching problem in the random-order semi-streaming setting. In this problem, the edges of an arbitrary n-vertex graph G = (V, E) arrive in a stream one by one and in a random order. The goal is to have a single pass over the stream, use O(n ⋅ polylog) space, and output a large matching of G.
We prove that for an absolute constant ε₀ > 0, one can find a (2/3 + ε₀)-approximate maximum matching of G using O(n log n) space with high probability. This breaks the natural boundary of 2/3 for this problem prevalent in the prior work and resolves an open problem of Bernstein [ICALP'20] on whether a (2/3 + Ω(1))-approximation is achievable.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol198-icalp2021/LIPIcs.ICALP.2021.19/LIPIcs.ICALP.2021.19.pdf
Maximum Matching
Streaming
Random-Order Streaming