Fast Deterministic Backtrack Search

The backtrack search problem involves visiting all the nodes of an arbitrary binary tree given a pointer to its root, subject to the constraint that the children of a node are revealed only after their parent is visited. This note describes a fast, deterministic backtrack search algorithm for a p-processor COMMON CRCW-PRAM that visits any n-node tree of height h in time O ((n/p + h)(log log log p)2). This upper bound compares favorably with a natural Ω(n/p + h) lower bound for this problem. Our approach embodies novel, efficient techniques for dynamically assigning tree-nodes to processors to ensure that the work is shared equitably among them.

[1]  Joseph JáJá,et al.  An Introduction to Parallel Algorithms , 1992 .

[2]  Frank Thomson Leighton,et al.  Coding theory, hypercube embeddings, and fault tolerance , 1991, SPAA '91.

[3]  Alan M. Frieze,et al.  Near-perfect Token Distribution , 1994, Random Struct. Algorithms.

[4]  Abhiram G. Ranade.  Optimal speedup for backtrack search on a butterfly network , 1991, SPAA '91.

[5]  Uri Zwick,et al.  Optimal deterministic approximate parallel prefix sums and their applications , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.

[6]  Richard Cole,et al.  Approximate Parallel Scheduling. Part I: The Basic Technique with Applications to Optimal Parallel List Ranking in Logarithmic Time , 1988, SIAM J. Comput..

[7]  Christos Kaklamanis,et al.  Branch-and-bound and backtrack search on mesh-connected arrays of processors , 1992, SPAA '92.

[8]  William Aiello,et al.  An atomic model for message-passing , 1993, SPAA '93.

[9]  S. Sitharama Iyengar,et al.  Introduction to parallel algorithms , 1998, Wiley series on parallel and distributed computing.

[10]  Frank Thomson Leighton,et al.  Dynamic Tree Embeddings in Butterflies and Hypercubes , 1992, SIAM J. Comput..

[11]  David S. Greenberg,et al.  Tight bounds for on-line tree embeddings , 1991, SODA '91.

[12]  Richard M. Karp,et al.  Randomized parallel algorithms for backtrack search and branch-and-bound computation , 1993, JACM.

[13]  Frank Thomson Leighton,et al.  Dynamic tree embeddings in butterflies and hypercubes , 1989, SPAA '89.

[14]  M KarpRichard,et al.  Randomized parallel algorithms for backtrack search and branch-and-bound computation , 1993 .

[15]  Abhiram G. Ranade.  A Simpler Analysis of the Karp-Zhang Parallel Branch-and-Bound Method , 1990 .