James Aspnes, Yossi Azar, Amos Fiat, Serge Plotkin, and Orli Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the Association for Computing Machinery 44(3):486–504, May 1997. An earlier version appeared in Twenty-Fifth Annual ACM Symposium on Theory of Computing, May 1993, pp. 623–631, under the title “On-line load balancing with applications to machine scheduling and virtual circuit routing.”
In this paper we study the problem of on-line allocation of routes to virtual circuits (both point-to-point 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(log n) 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(log n) factor. We also show that this result is tight, i.e. for any on-line algorithm there exists a scenario in which Ω(log n) increase in bandwidth is necessary in directed networks.
We view virtual circuit routing as a generalization of an on-line 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 maximum load.
For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrelated case (with n machines), we describe a new method that yields O(log n)-competitive algorithm. This stands in contrast to the natural greedy approach, whose competitive ratio is exactly n.
@article(AspnesAFPW1993,
title="On-line routing of virtual circuits with applications to load balancing and machine scheduling",
author="James Aspnes and Yossi Azar and Amos Fiat and Serge Plotkin and Orli Waarts",
journal=jacm,
volume=44,
number=3,
pages={486--504},
month=may,
year=1997
)