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Efficient Local Search with Conflict Minimization: A Case Study of the n-Queens Problem
October 1994 (vol. 6 no. 5)
pp. 661-668

Backtracking search is frequently applied to solve a constraint-based search problem, but it often suffers from exponential growth of computing time. We present an alternative to backtracking search: local search with conflict minimization. We have applied this general search framework to study a benchmark constraint-based search problem, the n-queens problem. An efficient local search algorithm for the n-queens problem was implemented. This algorithm, running in linear time, does not backtrack. It is capable of finding a solution for extremely large size n-queens problems. For example, on a workstation it can find a solution for 3000000 queens in less than 55 s.

[1] B. Abramson and M. Yung, "Divide and conquer under global constraints: A solution to then-queens problems,"J. Parallel Distrib. Computing, vol. 6, pp. 649-662, 1989.
[2] W. Ahrens,Mathematische Unterhaltungen und Spiele(in German). Leipzig, Germany: B. G. Teubner, 1918-1921.
[3] B. Bernhardsson, "Explicit solutions to then-queens problems for alln,"ACM SIGART Bull., vol. 2, p. 7, Apr. 1991.
[4] J. R. Bitner and E. M. Reingold, "Backtrack programming techniques,"Commun. ACM, vol. 18, no. 11, pp. 651-656, Nov. 1975.
[5] T.H. Cormen, C.E. Leiserson, and R.L. Rivest,Introduction to Algorithms, McGraw-Hill, Cambridge, Mass., 1990.
[6] B. J. Falkowski and L. Schmitz, "A note on the queens problem,"Inform. Processing Lett., vol. 23:39-46, July 1986.
[7] J. Gaschnig, "A constraint satisfaction method for inference making," inProc. 12th Ann. Allerton Conf. Circuit Syst. Theory, 1974.
[8] J. Gaschnig, "Performance measurement and analysis of certain search algorithms," Ph.D. thesis, Carnegie-Mellon Univ., Comput. Sci. Dept., Pittsburgh, PA, 1979.
[9] J. Gu, "Parallel algorithms and architectures for very fast search," Tech. Rep. UUCS-TR-88-005, Ph.D. dissertation, Univ. of Utah, Dept. of Comput. Sci., July 1988.
[10] J. Gu, "How to solve very large-scale satisfiability (VLSS) problems," Tech. Rep., 1988 (present in part in J. Gu, "Benchmarking SAT algorithms," Tech. Rep. UCECE-TR-90-002, 1990).
[11] J. Gu, "On a general framework for large-scale constraint-based optimization,"SIGART Bull., vol. 2, p. 8, Apr. 1991.
[12] J. Gu, "Efficient local search for very large-scale satisfiability problem,"SIGART Bull., vol. 3, pp. 8-12, Jan. 1992.
[13] J. Gu, "Benchmarking SAT algorithms," Tech. Rep. UCECE-TR-90- 002, Oct. 1990.
[14] J. Gu,Contraint-Based Search. New York: Cambridge University Press, 1995 (in press).
[15] R. M. Haralick and G. Elliot, "Increasing tree search efficiency for constraint satisfaction problems,"Artificial Intell., vol. 14, pp. 263-313, 1980.
[16] E. J. Hoffman, J. C. Loessi, and R. C. Moore, "Constructions for the solution of thenqueens problem,"Mathemat. Mag., 1969, pp. 66-72.
[17] L. Johnson, editor letter,SIGART Bull., Oct. 1990 to Oct. 1991.
[18] L. V. Kalé, "An almost perfect heuristic for thennonattacking queens problem,"Inform. Processing Lett., vol. 34, pp. 173-178, Apr. 1990.
[19] S. Minton, M. D. Johnston, A. B. Philips, and P. Laird, "Solving large-scale constraint satisfaction and scheduling problems using a heuristic repair method," inProc. AAAI90, 1990, pp. 17-24.
[20] P. W. Purdom and C. A. Brown, "An analysis of backtracking with search rearrangement,"SIAM J. Comput., vol. 12, no. 4, pp. 717-733, Nov. 1983.
[21] P. W. Purdom, C. A. Brown, and E. L. Robertson, "Backtracking with multi-level dynamic search rearrangement,"Acta Informatica, vol. 15, pp. 99-113, 1981.
[22] M. Reichling, "A simplified solution of thenqueens problem,"Inform. Processing Lett., vol. 25, pp. 253-255, June 1987.
[23] R. Sosic and J. Gu, "How to search for million queens," Tech. Rep. UUCS-TR-88-008, Dept. of Comput. Sci., Univ. of Utah, Feb. 1988.
[24] R. Sosic and J. Gu, "Fast search algorithms for then-queens problem,"IEEE Trans. Syst., Man, Cybernetics, vol. 21, pp. 1572-1576, Nov./Dec. 1991.
[25] R. Sosic and J. Gu, "A polynomial time algorithm for then-queens problem,"SIGART Bull., vol. 1, no. 3, pp. 7-11, Oct. 1990.
[26] R. Sosic and J. Gu, "3,000,000 queens in less than a minute,"SIGART Bull., vol. 2, no. 2, pp. 22-24, Apr. 1991.
[27] H. S. Stone and J. M. Stone, "Efficient search techniques: An empirical study of then-queens problem,"IBM J. Res. Dev., vol. 31, no. 4, pp. 464-474, July 1987.

Index Terms:
operations research; search problems; minimisation; constraint handling; local search; conflict minimization; n-queens problem; backtracking search; constraint-based search problem; exponential growth; computing time; benchmark constraint-based search problem; local search algorithm; linear time; large size n-queens problems; workstation; nonbacktracking search
Citation:
R. Sosic, J. Gu, "Efficient Local Search with Conflict Minimization: A Case Study of the n-Queens Problem," IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 661-668, Oct. 1994, doi:10.1109/69.317698
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