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SIAM J. COMPUT. c 2008 Society for Industrial and Applied Mathematics
Vol. 37, No. 5, pp. 16561673
STABILITY OF LOAD BALANCING ALGORITHMS IN
DYNAMIC ADVERSARIAL SYSTEMS
ELLIOT ANSHELEVICH, DAVID KEMPE, AND JON KLEINBERG§
Abstract. In the dynamic load balancing problem, we seek to keep the job load roughly evenly
distributed among the processors of a given network. The arrival and departure of jobs is modeled
by an adversary restricted in its power. Muthukrishnan and Rajaraman [An adversarial model
for distributed dynamic load balancing, in Proceedings of the 10th ACM Symposium on Parallel
Algorithms and Architectures, ACM, New York, 1998] gave a clean characterization of a restriction
on the adversary that can be considered the natural analogue of a cut condition. They proved that a
simple local balancing algorithm proposed by Aiello et al. [Approximate load balancing on dynamic
and asynchronous networks, in Proceedings of the 25th ACM Symposium on Theory of Computing,
ACM, New York, 1993] is stable against such an adversary if the insertion rate is restricted to a
(1  ) fraction of the cut size. They left as an open question whether the algorithm is stable at
rate 1. In this paper, we resolve this question positively, by proving stability of the local algorithm at
rate 1. Our proof techniques are very different from the ones used by Muthukrishnan and Rajaraman
and yield a simpler proof and tighter bounds on the difference in loads. In addition, we introduce
a multicommodity version of this load balancing model and show how to extend the result to the
