An Efficient Mean Field Annealing Formulation for Mapping Unstructured Domains to Hypercubes

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 + P2) 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 Nlg2P and Θ(d avg lg2P+Plg2P), respectively, by exploiting the topological properties of hypercubes.