An optimal deterministic algorithm for online b-matching

Abstract We consider the natural online version of the well-known unweighted b -matching problem. We present a deterministic algorithm B ALANCE whose competitive ratio is 1−1/(1+1/b) a , where a is the number of online servers per site, and b is the number of adversarial servers per site. We show that the competitive ratio of every deterministic online algorithm is at least 1−1/(1+1/b) a . Hence, B ALANCE is optimally competitive, including low-order terms. In the case a=b , the competitive ratio of B ALANCE approaches 1−1/e≈0.63 as b grows.