Online load balancing and network flow
Steven D. Phillips, Jeffery Westbrook · 1993
In this paper we study two problems that can be viewed as on-line games on a dynamic bipartite graph. The first problem is on-line load balancing with preemption. A centralized scheduler must assign tasks to servers, processing online a sequence of task arrivals and departures. Each task is restricted to run on some subset of the servers. The scheduler attempts to keep the load well-balanced. If preemptive reassignments are dissallowed, Azar, Broder and Karlin [3] proved a lower bound of \\Omega\\Gamma p n) on the ratio between the maximum load achieved by an on-line algorithm and the optimum off-line maximum load. We show that this ratio can be greatly reduced by an efficient scheduler using only a small amount of rescheduling. We then apply these ideas to network flow. Cheriyan and Hagerup [6] introduced an on-line game on a bipartite graph as a fundamental step in improving algorithms for computing the maximum flow in networks. They described a randomized strategy to play the game. ...