Abstract

We study the online unweighted b-matching problem where at most b 1 requests can be matched to any server site. We present a deterministic algorithm Balance whose competitive ratio is 1 \Gamma 1 (1+ 1 b ) b . We show that the competitive ratio of every deterministic online algorithm is at least 1 \Gamma 1 (1+ 1 b ) b . Hence, Balance is optimally competitive, including low order terms. For large b, the competitive ratio of Balance approaches 1 \Gamma 1 e ß :63. 1 Introduction We consider the natural online version of the well-known b-matching problem on an unweighted bipartite graph G = (S; R; E), where S and R are the vertex partitions and E is the edge set. At the ith unit of time, 1 i n, the vertex r i 2 R and all the edges incident to r i are revealed to the online algorithm A. A then must either decline to ever service r i , or irrevocably select a site s k adjacent to r i in G to service r i . No server site may be used more than b times. Hence, it may well not b...

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