Combining Online Algorithms for Acceptance and Rejection

Resource allocation and admission control are critical tasks in a communication network that often must be performed online. Algorithms for these types of problems have been considered both under benefit models (e.g., with a goal of approximately maximizing the number of requests accepted) and under cost models (e.g., with a goal of approximately minimizing the number of requests rejected). Unfortunately, algorithms designed for these two measures can often be quite different, even polar opposites. In this work we consider the problem of combining algorithms designed for each of these objectives in a way that is good under both measures simultaneously. More formally, we are given an algorithm A that is cA competitive with respect to the number of accepted requests and an algorithm R that is cR competitive with respect to the number of rejected requests. We show how to derive a combined algorithm with competitive ratio O(cRcA) for rejection and O(cA) for acceptance. We also build on known techniques to show that given a collection of k algorithms, we can ∗Research supported in part by the Israel Science Foundation and by the IST Program of the EU. †Research supported in part by NSF grants CCR-0105488, CCR-0122581, ITR IIS-0121678 and by a BSF grant. ‡Research supported in part by NSF grant CCR-0093348. §Research supported in part by the Israel Science Foundation (grant No. 1079/04) and by a BSF grant. ACM Classification: F.2.2, C.2.2 AMS Classification: 68W05