The problem of load balancing on the hypercube is considered. A number of tokens are placed at the nodes and the goal is to redistribute them evenly throughout the network. Initially each of the p nodes stores up to m tokens. A simple algorithm is presented operating in time O(logp + m log log p) on average. Introduction A distributed-memory multicomputer system consists of nodes interconnected by a message-passing network. The nodes are processing elements capable of performing autonomous

more »

... tations. They communicate with neighboring nodes by transmitting and receiving packets. The packets may carry specifications of independent tasks to be performed at the receiving nodes. We consider a situation when the tasks are first created by the nodes individually, then the nodes communicate with the others to see how much work there is to be done, then the tasks are redistributed among the nodes. We concentrate on the stage of distributing tasks among the processors, which is often called load balancing. The problem of load balancing has been studied extensively for various kinds of networks, including hypercubes [6, 11, 12, 13] , meshes [8] , and expanders [2, 5, 9, 10] . There was also work on arbitrary network topologies [1, 3, 4] . We present a new simple and easy to implement algorithm on the hypercube with a competitive performance for the case of relatively small initial distribution of tasks among the processors. Problem and model of computation. The following properties, that restrict the general problem of redistributing work among the processors, are assumed in this paper: