Distributing Unit Size Workload Packages in Heterogeneous Networks

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 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. Article Type Communicated by Submitted Revised regular paper Tomasz Radzik September 2004 April 2005 This work was partly supported by the German Research Foundation (DFG) project SFB-376 and by the IST Program of the EU under contract numbers IST-1999-14186 (ALCOM-FT) and IST-2001-33116 (FLAGS). Parts of the results have been presented at the European Symposium on Algorithms 2004 [10]. R. Elsässer et al., Load Balancing in Networks, JGAA, 10(1) 51–68 (2006) 52