A Scalable Diffusion Algorithm for Dynamic Mapping and Load Balancing on Networks of Arbitrary Topology

Abstract

The problems of mapping and load balancing applications on arbitrary networks are considered. A novel diffusion algorithm is presented to solve the mapping problem. It complements the well known diffusion algorithms for load balancing which have enjoyed success on massively parallel computers (MPPs). Mapping is more difficult on interconnection networks than on MPPs because of the variations which occur in network topology. Popular mapping algorithms for MPPs which depend on recursive topologies are not applicable to irregular networks. The most celebrated of these MPP algorithms use information from the Laplacian matrix of a graph of communicating processes. The diffusion algorithm presented in this paper is also derived from this Laplacian matrix. The diffusion algorithm works on arbitrary network topologies and is dramatically faster than the celebrated MPP algorithms. It is delay and fault tolerant. Time to convergence depends on initial conditions and is insensitive to problem scale. This excellent scalability, among other features, makes the diffusion algorithm a viable candidate for dynamically mapping and load balancing not only existing MPP systems but also large distributed systems like the Internet, small cluster computers, and networks of workstations.