Combining Online Algorithms for Acceptance and Rejection

Abstract

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 $c_A$ competitive with respect to the number of accepted requests and an algorithm $R$ that is $c_R$ competitive with respect to the number of rejected requests. We show how to derive a combined algorithm with competitive ratio $O(c_R c_A)$ for rejection and $O(c_A)$ for acceptance. We also build on known techniques to show that given a collection of $k$ algorithms, we can construct one master algorithm that performs similarly to the best algorithm among the $k$ for the acceptance problem and another master algorithm that performs similarly to the best algorithm among the $k$ for the rejection problem. Using our main result we can combine the two master algorithms to a single algorithm that guarantees both rejection and acceptance competitiveness.