 
Summary: OnLine Routing of Virtual Circuits with
Applications to Load Balancing and Machine
Scheduling \Lambda
James Aspnes y Yossi Azar z Amos Fiat x
Serge Plotkin  Orli Waarts k
Abstract
In this paper we study the problem of online allocation of routes to virtual circuits (both
pointtopoint and multicast) where the goal is to route all requests while minimizing the
required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a
circuit is established, it exists forever), and describe an algorithm that achieves an O(logn)
competitive ratio with respect to maximum congestion, where n is the number of nodes in
the network. Informally, our results show that instead of knowing all of the future requests,
it is sufficient to increase the bandwidth of the communication links by an O(logn) factor.
We also show that this result is tight, i.e. for any online algorithm there exists a scenario
in which
\Omega\Gamma137 n) increase in bandwidth is necessary in directed networks.
We view virtual circuit routing as a generalization of an online load balancing problem,
defined as follows: jobs arrive on line and each job must be assigned to one of the machines
immediately upon arrival. Assigning a job to a machine increases this machine's load by
an amount that depends both on the job and on the machine. The goal is to minimize the
