 
Summary: Admission Control to Minimize Rejections and Online Set Cover
with Repetitions
Noga Alon # Yossi Azar + Shai Gutner #
Abstract
We study the admission control problem in general networks. Communication requests arrive over
time, and the online algorithm accepts or rejects each request while maintaining the capacity limitations
of the network. The admission control problem has been usually analyzed as a benefit problem, where the
goal is to devise an online algorithm that accepts the maximum number of requests possible. The problem
with this objective function is that even algorithms with optimal competitive ratios may reject almost all
of the requests, when it would have been possible to reject only a few. This could be inappropriate for
settings in which rejections are intended to be rare events.
In this paper, we consider preemptive online algorithms whose goal is to minimize the number of
rejected requests. Each request arrives together with the path it should be routed on. We show an
O(log 2 (mc))competitive randomized algorithm for the weighted case, where m is the number of edges
in the graph and c is the maximum edge capacity. For the unweighted case, we give an O(log m log c)
competitive randomized algorithm. This settles an open question of Blum, Kalai and Kleinberg raised in
[10]. We note that allowing preemption and handling requests with given paths are essential for avoiding
trivial lower bounds.
The admission control problem is a generalization of the online set cover with repetitions problem,
whose input is a family of m subsets of a ground set of n elements. Elements of the ground set are given
