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Evaluation of a Parallel Branch-and-Bound Algorithm on a Class of Multiprocessors
January 1994 (vol. 5 no. 1)
pp. 74-86

We propose and evaluate a parallel "decomposite best-first" search branch-and-boundalgorithm (dbs) for MIN-based multiprocessor systems. We start with a new probabilisticmodel to estimate the number of evaluated nodes for a serial best-first searchbranch-and-bound algorithm. This analysis is used in predicting the parallel algorithmspeed-up. The proposed algorithm initially decomposes a problem into N subproblems,where N is the number of processors available in a multiprocessor. Afterwards, eachprocessor executes the serial best-first search to find a local feasible solution. Localsolutions are broadcasted through the network to compute the final solution. Aconflict-free mapping scheme, known as the step-by-step spread, is used for subproblemdistribution on the MIN. A speedup expression for the parallel algorithm is then derivedusing the serial best-first search node evaluation model. Our analysis considers bothcomputation and communication overheads for providing realistic speed-up.Communication modeling is also extended for the parallel global best-first searchtechnique. All the analytical results are validated via simulation. For large systems, whencommunication overhead is taken into consideration, it is observed that the paralleldecomposite best-first search algorithm provides better speed-up compared to otherreported schemes.

[1] E. L. Lawler and D. W. Wood, "Branch-and-bound methods: A survey,"Oper. Res., vol. 14, pp. 699-719, 1966.
[2] E. Horowitz and S. Sahni,Fundamentals of Computer Algorithms. Rockville, MD: Computer Sci. Press, 1978.
[3] A. Aho, J. Hopcroft, and J. Ullman,Data Structures and Algorithms. Reading, MA: Addison-Wesley, 1983.
[4] D. R. Smith, "Random trees and the analysis of branch-and-bound procedures,"J. ACM, vol. 31, no. 1, pp. 163-188, 1984.
[5] B. W. Wah and C. F. Yu, "Stochastic modeling of branch-and-bound algorithms with best-first search,"IEEE Trans. Software Eng., vol. SE-11, no. 9, pp. 922-934, Sept. 1985.
[6] V. K. Janakiram, D. P. Agrawal, and R. Mehrotra, "A randomized parallel branch-and-bound algorithm," inProc. Int. Conf. Parallel Process., Aug. 1988, pp. 69-75.
[7] B. W. Wah and Y. W. Eva Ma, "MANIP--A multicomputer architecture for solving combinatorial extremum-search problems,"IEEE Trans. Comput., vol. C-33, pp. 377-390, May 1984.
[8] G.-J. Li and B. W. Wah, "Computational efficiency of parallel approximate branch-and-bound algorithm," inProc. Int. Conf. Parallel Process., Aug. 1984, pp. 473-480.
[9] V. Kumar and V. N. Rao, "Parallel depth-first search, Part II: Analysis,"Int. J. Parallel Program., vol. 16, no. 6, pp. 501-519, 1987.
[10] V. Kumar and V. N. Rao, "Parallel depth-first search ring architecture," inProc. Int. Conf. Parallel Process., Aug. 1988, pp. 128-132.
[11] O. I. El-Dessouki and W. H. Huen, "Distributed enumeration on between computers,"IEEE Trans. Comput., vol. C-29, pp. 818-825, Sept. 1980.
[12] R. M. Karp and Y. Zhang, "A randomized parallel branch-and-bound procedure," inProc. ACM Symp. Theory Comput., May 1988, pp. 290-300.
[13] M. J. Quinn, "Analysis and implementation of branch-and-bound algorithms on a hypercube multicomputer,"IEEE Trans. Comput., vol. C-39, pp. 384-387, Mar. 1990.
[14] J. Mohan, "Experience with two parallel programs solving the traveling salesman problem," inProc. Int. Conf. Parallel Process., Aug. 1983, pp. 191-193.
[15] T.H. Lai and S. Sahni, "Anomalies in Parallel Branch-and-Bound Algorithms,"Comm. ACM, June 1984, pp. 594-602.
[16] T.-H. Lai and S. Sahni, "Butterfly GP1000--Overview," BBN Advanced Computer Inc., Nov. 1988.

Index Terms:
Index Termsmultiprocessor interconnection networks; multiprocessing systems; parallel algorithms;performance evaluation; parallel branch-and-bound algorithm; MIN-based multiprocessorsystems; probabilistic model; serial best-first search; conflict-free mapping scheme;communication overheads; computation overheads
Citation:
M.K. Yang, C.R. Das, "Evaluation of a Parallel Branch-and-Bound Algorithm on a Class of Multiprocessors," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 1, pp. 74-86, Jan. 1994, doi:10.1109/71.262590
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