An efficient mean field annealing formulation for mapping unstructured domains to hypercubes

Abstract

We propose an efficient MFA formulation for mapping unstructured domains to hypercube-connected distributed-memory architectures. In the general MFA formulation, N×P spin variables are maintained and an individual MFA iteration requires Θ(d _avg P + P ²) time for the mapping of a sparse domain graph with N vertices and average vertex degree of d _avg to a parallel architecture with P processors. The proposed hypercube-specific MFA formulation asymptotically reduces the number of spin variables and the computational complexity of an individual MFA iteration to Nlg ₂ P and Θ(d _avg lg ₂ P+Plg ₂ P), respectively, by exploiting the topological properties of hypercubes.

This work is partially supported by the Commission of the European Communities, Directorate General for Industry under contract ITDC 204-82166.