 
Summary: Combining Online Algorithms for Rejection and Acceptance
Yossi Azar Avrim Blum y Yishay Mansour z
May 28, 2003
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 benet models (e.g., with a goal of approximately maximizing the number of calls
accepted) and under cost models (e.g., with a goal of approximately minimizing the number of
calls rejected). Unfortunately, algorithms designed for these two measures can often be quite
dierent, even polar opposites (e.g., [1, 8]). In this work we consider the problem of combining
algorithms designed for each of these objectives in a way that simultaneously is good under both
measures. More formally, we are given an algorithm A which is c A competitive w.r.t. the number
of accepted calls and an algorithm R which is c R competitive w.r.t. the number of rejected calls.
We derive a combined algorithm whose competitive ratio is O(cR c A ) for rejection and O(c 2
A ) for
acceptance. We also show building on known techniques that given a collection of k algorithms,
we can construct one master algorithm which performs similar to the best algorithm among the
k for the acceptance problem and another master algorithm which performs similar 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 which guarantees both rejection and acceptance
