An Asymptotically Optimal Algorithm for Maximum Matching in Dynamic Streams

Abstract

We present an algorithm for the maximum matching problem in dynamic (insertion-deletions) streams with asymptotically optimal space complexity: for any n-vertex graph, our algorithm with high probability outputs an α-approximate matching in a single pass using O(n 2 /α 3 ) bits of space.A long line of work on the dynamic streaming matching problem has reduced the gap between space upper and lower bounds first to n o(1) factors [Assadi-Khanna-Li-Yaroslavtsev; SODA 2016] and subsequently to polylog(n) factors [Dark-Konrad; CCC 2020]. Our upper bound now matches the Dark-Konrad lower bound up to O(1) factors, thus completing this research direction.