Parallel Processing of Discrete Optimization Problems

Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Often, a DOP is formulated in terms of nding a (minimum cost) solution path in a graph from an initial node to a goal node and solved by graph/tree search methods such as branch-and-bound and dynamic programming. Availability of parallel computers has created substantial interest in exploring the use of parallel processing for solving discrete optimization problems. This article provides an overview of parallel search algorithms for solving discrete optimization problems.

[1]  Richard E. Korf,et al.  Depth-First Iterative-Deepening: An Optimal Admissible Tree Search , 1985, Artif. Intell..

[2]  Catherine Roucairol,et al.  A parallel branch and bound algorithm for the quadratic assignment problem , 1987, Discret. Appl. Math..

[3]  Oliver Vornberger,et al.  Superlinear Speedup for Parallel Backtracking , 1987, ICS.

[4]  Herbert S. Wilf,et al.  Algorithms and Complexity , 1994, Lecture Notes in Computer Science.

[5]  Vipin Kumar,et al.  Automatic Test Pattern Generation on Multiprocessors: A Summary of Results , 1989, KBCS.

[6]  Richard E. Korf,et al.  Distributed Tree Search and Its Application to Alpha-Beta Pruning , 1988, AAAI.

[7]  Vipin Kumar,et al.  A Parallel Implementation of Iterative-Deepening-A* , 1987, AAAI.

[8]  L. N. Kanal,et al.  The CDP: A unifying formulation for heuristic search, dynamic programming, and branch-and-bound , 1988 .

[9]  P. B. Coaker,et al.  Applied Dynamic Programming , 1964 .

[10]  V. Nageshwara Rao,et al.  Scalable parallel formulations of depth-first search , 1990 .

[11]  T. N. Mudge,et al.  Parallel branch and bound algorithms on hypercube multiprocessors , 1989, C3P.

[12]  Douglas R. Smith,et al.  Random Trees and the Analysis of Branch and Bound Procedures , 1984, JACM.

[13]  Vipin Kumar,et al.  Floorplan optimization on multiprocessors , 1989, Proceedings 1989 IEEE International Conference on Computer Design: VLSI in Computers and Processors.

[14]  M. Held,et al.  Finite-State Processes and Dynamic Programming , 1967 .

[15]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[16]  J. L. Calvet,et al.  Vectorization and multitasking of dynamic programming in control: experiments on a CRAY-2 , 1990, Parallel Comput..

[17]  Vipin Kumar,et al.  Unstructured Tree Search on SIMD Parallel Computers , 1994, IEEE Trans. Parallel Distributed Syst..

[18]  Masakazu Furuichi,et al.  A multi-level load balancing scheme for OR-parallel exhaustive search programs on the multi-PSI , 1990, PPOPP '90.

[19]  Richard E. Korf,et al.  Single-Agent Parallel Window Search: A Summary of Results , 1989, IJCAI.

[20]  Panos M. Pardalos,et al.  A parallel algorithm for the quadratic assignment problem , 1989, Proceedings of the 1989 ACM/IEEE Conference on Supercomputing (Supercomputing '89).

[21]  Oliver Vornberger,et al.  Implementing Branch-and-Bound in a Ring of Processors , 1986, CONPAR.

[22]  Vipin Kumar,et al.  Parallel Algorithms for Machine Intelligence and Vision , 2011, Symbolic Computation.

[23]  H. T. Kung,et al.  Direct VLSI Implementation of Combinatorial Algorithms , 1979 .

[24]  P. Gilmore Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem , 1962 .

[25]  Kai Hwang Advanced Computer Architecture with Parallel Programming , 1993 .

[26]  P. Pardalos,et al.  Parallel branch and bound algorithms for quadratic zero–one programs on the hypercube architecture , 1990 .

[27]  Benjamin W. Wah,et al.  Multiprocessing of Combinatorial Search Problems , 1985, Computer.

[28]  Harold S. Stone,et al.  The Average Complexity of Depth-First Search with Backtracking and Cutoff , 1986, IBM J. Res. Dev..

[29]  Ellis Horowitz,et al.  Fundamentals of Computer Algorithms , 1978 .

[30]  Laxmikant V. Kalé,et al.  A dynamic scheduling strategy for the Chare-Kernel system , 1989, Proceedings of the 1989 ACM/IEEE Conference on Supercomputing (Supercomputing '89).

[31]  Vipin Kumar,et al.  Parallel Branch-and-Bound Formulations for AND/OR Tree Search , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[33]  R. Burkard,et al.  Assignment and Matching Problems: Solution Methods with FORTRAN-Programs , 1980 .

[34]  Benjamin W. Wah,et al.  Coping with Anomalies in Parallel Branch-and-Bound Algorithms , 1986, IEEE Transactions on Computers.

[35]  Vipin Kumar,et al.  Scalable Load Balancing Techniques for Parallel Computers , 1994, J. Parallel Distributed Comput..

[36]  Sartaj Sahni,et al.  Hypercube algorithms for image processing and pattern recognition , 1990 .

[37]  Michael J. Quinn,et al.  Analysis and Implementation of Branch-and Bound Algorithms on a Hypercube Multicomputer , 1990, IEEE Trans. Computers.

[38]  John P. Fishburn,et al.  Parallelism in Alpha-Beta Search , 1982, Artif. Intell..

[39]  William A. Kornfeld The Use of Parallelism to Implement a Heuristic Search , 1981, IJCAI.

[40]  Panos M. Pardalos,et al.  Topics in parallel computing in mathematical programming , 1993, Applied discrete mathematics and theoretical computer science.

[41]  A. Gottleib,et al.  The nyu ultracomputer- designing a mimd shared memory parallel computer , 1983 .

[42]  Michael J. Quinn,et al.  Designing Efficient Algorithms for Parallel Computers , 1987 .

[43]  Larry S. Davis,et al.  Parallel Iterative A* Search: An Admissible Distributed Heuristic Search Algorithm , 1989, IJCAI.

[44]  K. Hoffman,et al.  Large-scale 0–1 linear programming on distributed workstations , 1990 .

[45]  Thomas E. Vollmann,et al.  An Experimental Comparison of Techniques for the Assignment of Facilities to Locations , 1968, Oper. Res..

[46]  Afonso Ferreira,et al.  A massively parallel knowledge-base server using a hypercube multiprocessor , 1990, [1990] Proceedings of the 2nd International IEEE Conference on Tools for Artificial Intelligence.

[47]  Sartaj Sahni,et al.  A Hypercube Algorithm for the 0/1 Knapsack Problem , 1988, J. Parallel Distributed Comput..

[48]  Sartaj Sahni,et al.  Anomalies in Parallel Branch-and-Bound Algorithms , 1984 .

[49]  Vipin Kumar,et al.  Efficient parallel algorithms for search problems: applications in VLSI CAD , 1990, [1990 Proceedings] The Third Symposium on the Frontiers of Massively Parallel Computation.

[50]  Laxmikant V. Kalé,et al.  Consistent Linear Speedups to a First Solution in Parallel State-Space Search , 1990, AAAI.

[51]  Laveen N. Kanal,et al.  A Hybrid SSS*/Alpha-Beta Algorithm for Parallel Search of Game Trees , 1985, IJCAI.

[52]  Benjamin W. Wah,et al.  The status of manip - a multicomputer architecture for solving, combinatorial extremum-search problems , 1984, ISCA '84.

[53]  Judea Pearl,et al.  Heuristics : intelligent search strategies for computer problem solving , 1984 .

[54]  Vipin Kumar,et al.  Parallel Best-First Search of State-Space Graphs: A Summary of Results , 1988, AAAI.