Deterministic branch-and-bound on distributed memory machines

Extended abstract
  • Kieran T. Herley
  • Andrea Pietracaprina
  • Geppino Pucci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1586)

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+hlog4p) 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.

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Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Kieran T. Herley
    • 1
  • Andrea Pietracaprina
    • 2
  • Geppino Pucci
    • 2
  1. 1.Department of Computer ScienceUniversity College CorkCorkIreland
  2. 2.Dipartimento di Elettronica e InformaticaUniversítà di PadovaPadovaItaly

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