Abstract
In this paper we investigate the parallel complexity of backtrack and branch-and-bound search on the mesh-connected array. We present an Ω(√dN/√logdN) lower bound for the time needed by arandomized algorithm to perform backtrack and branch-and-bound search of a tree of depthd on the √N × √N mesh, even when the depth of the tree is known in advance. The lower bound also holds for algorithms that are allowed to move tree-nodes and create multiple copies of the same tree-node.
For the upper bounds we givedeterministic algorithms that are within a factor of 0(log3/2 N) from our lower bound. Our algorithms do not make any assumption on the shape of the tree to be searched, do not know the depth of the tree in advance, and do not move tree-nodes nor create multiple copies of the same node.
The best previously known algorithm for backtrack search on the mesh was randomized and required Θ(d√N/ logN) time. Our algorithm for branch-and-bound is the first algorithm that performs branch-and-bound search on a sparse network. Both the lower and the upper bounds extend to meshes of higher dimensions.
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Part of this work was done while the authors were at Harvard University.
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Kaklamanis, C., Persiano, G. Branch-and-bound and backtrack search on mesh-connected arrays of processors. Math. Systems Theory 27, 471–489 (1994). https://doi.org/10.1007/BF01184935
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DOI: https://doi.org/10.1007/BF01184935