Deterministic branch-and-bound on distributed memory machines

Abstract

The branch-and-bound problem involves determining the leaf of minimum cost in a cost-labelled, heap-ordered tree, subject to the constraint that only the root is known initially and that the children of each node are revealed only by visiting their parent. We present the first efficient deterministic algorithm to solve the branch-and-bound problem for a tree T of constant degree on a p-processor Distributed-Memory Machine. Let c ^* be the cost of the minimumcost leaf in T, and let n and h be the number of nodes and the height, respectively, of the subtree T ^*⊆T of nodes whose cost is at most c ^*. When accounting for both computation and communication costs, our algorithm runs in time O(n/p+h(max{p, log n log p})²) for general values of n, and can be made to run in time O ((n/p+hlog⁴ p) log log p) for n polynomial in p. For large ranges of the relevant parameters, our algorithm is provably optimal or outperforms the well-known randomized strategy by Karp and Zhang.

This research was supported, in part, by the CNR of Italy under Grant CNR97.03207.CT07 Load Balancing and Exhausive Search Techniques for Parallel Architectures.