Improved Algorithm for Dynamic b-Matching

Recently there has been extensive work on maintaining (approximate) maximum matchings in dynamic graphs. We consider a generalisation of this problem known as themaximum b-matching: Every node v has a positive integral capacity bv, and the goal is to maintain an (approximate) maximum-cardinality subset of edges that contains at most bv edges incident on every node v. The maximum matching problem is a special case of this problem where bv = 1 for every node v. Bhattacharya, Henzinger and Italiano [ICALP ’15] showed how to maintain a O(1) approximate maximum b-matching in a graph in O(log3 n) amortised update time. Their approximation ratio was a large (double digit) constant. We significantly improve their result both in terms of approximation ratio as well as update time. Specifically, we design a randomised dynamic algorithm that maintains a (2 + )-approximate maximum b-matching in expected amortised O(1/ 4) update time. Thus, for every constant ∈ (0, 1), we get expected amortised O(1) update time. Our algorithm generalises the framework of Baswana, Gupta, Sen [FOCS ’11] and Solomon [FOCS ’16] for maintaining a maximal matching in a dynamic graph. 1998 ACM Subject Classification F.2 Analysis of Algorithms and Problem Complexity