Load balancing of indivisible unit size tokens in dynamic and heterogeneous networks

Abstract. The task of balancing dynamically generated work load occurs in a wide range of parallel and distributed applications. Diffusion based schemes, which belong to the class of nearest neighbor load balancing algorithms, are a popular way to address this problem. Originally created to equalize the amount of arbitrarily divisible load among the nodes of a static and homogeneous network, they have been generalized to heterogeneous topologies. Additionally, some simple diffusion algorithms have been adapted to work in dynamic networks as well. However, if the load is not divisible arbitrarily but consists of indivisible unit size tokens, diffusion schemes are not able to balance the load properly. In this paper we consider the problem of balancing indivisible unit size tokens on dynamic and heterogeneous systems. By modifying a randomized strategy invented for homogeneous systems, we can achieve an asymptotically minimal expected overload in l1, l2 and l ∞ norm while only slightly increasing the run-time by a logarithmic factor. Our experiments show that this additional factor is usually not required in applications.