Analysis of nearest neighbor load balancing algorithms for random loads Peter Sanders * ,1 Max-Planck-Institut f  ur Informatik, Im Stadtwald, 66123 Saarbr ucken, Germany Abstract Nearest neighbor load balancing algorithms, like diusion, are popular due to their sim- plicity, ¯exibility, and robustness. We show that they are also asymptotically very ecient when a random rather than a worst case initial load distribution is considered. We show that diusion needs Hlog n 2=d  balancing time on a d -dimensional mesh network with n d pro- cessors. Furthermore, some but not all of the algorithms known to perform better than dif- fusion in the worst case also perform better for random loads. We also present new results on worst case performance regarding the maximum load deviation. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Parallel algorithm analysis; Nearest neighbor load balancing algorithm; Load balancing random loads; Maximum load deviation; Diusion load balancing 1. Introduction Load balancing is one of the key aspects of parallel computing. The problem has so many aspects that abstract models are important for separating a load balancing algorithm from the machine and the particular application used. One interesting load model is the following: the load of a processor (PE) can be accurately deter- mined and arbitrarily subdivided into multiple pieces which can be independently worked on by dierent PEs. Any portion of load can be communicated to a neighboring PE in unit time. A related model assumes the load to consist of discrete, equally sized load units and transmission costs which are proportional to the number of units transferred. www.elsevier.com/locate/parco Parallel Computing 25 (1999) 1013±1033 * E-mail: sanders@mpi-sb.mpg.de 1 Most of this work was done while the author was at the University of Karlsruhe. 0167-8191/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 8 1 9 1 ( 9 9 ) 0 0 0 4 0 - X