Backtrack searching in the presence of symmetry

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 357 LNCS, Issue , 1989, Pages 99-110

  Brown, Cynthia A ^a   Finkelstein, Larry ^a   Purdom, Paul Walton ^b  

^a NORTHEASTERN UNIVERSITY   (United States)

^b INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; GROUP THEORY;

AUTOMORPHISMS; COMPUTATIONAL GROUP THEORY; DYNAMIC SEARCH; SEARCH PROBLEM; SEARCH SPACES; SYMMETRY GROUPS; TESTING ALGORITHM;

ALGEBRA;

EID: 84987216875     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-51083-4_51     Document Type: Conference Paper

References (21)

1. James R. Bitner and Edward M. Reingold, “Backtrack Programming Techniques”, CACM 18 (1975), pp. 121-136.
2. Roger W. Brockett and David Dobkin, “On the Number of Multiplications Required for Matrix Multiplication”, SIAM J. Comput. 5 (1976), pp. 624-628.
3. C. A. Brown, L. A. Finkelstein, and P. W. Purdom Jr., “Backtrack Searching in the Presence of Symmetry”, NUTR NU-CCS-87-2 (1987).
4. C. A. Brown, L. A. Finkelstein, and P. W. Purdom Jr., “Efficient Implementation of Jerrum’s Algorithm for Permutation Groups”, NUTR NU-CCS-87-19 (1987).
5. C. A. Brown, L. A. Finkelstein, and P. W. Purdom Jr., “A New Base Change Algorithm for Permutation Groups”, NUTR NU-CCS-87-30 (1987).
6. G. Butler, “Computing in Permutation and Matrix Groups II: Backtrack Algorithm”, Math. Comp. 39 (1982), pp. 671-680.
7. G. Butler and C. W. H. Lam, “A General Backtrack Algorithm for the Isomorphism Problem of Combinatorial Objects”, Journal of Symbolic Computation 1 (1985), pp. 363-382.
8. J. J. Cannon, “An Introduction to the Group Theory Language, Cayley”, in Computational Group Theory, edited by M. D. Atkinson, Academic Press, 1984, pp. 145-184.
9. J. L. Carter, On the Existence of a Projective Plane of Order 10, Ph. D. Thesis, University of California at Berkeley (1974).
10. J. W. L. Glaisher, “On the Problem of the Eight Queens”, Philosophical Magazine series 4, rot. 48 (1874), pp. 457-467.
11. Shaft Goldwasser and Michael Sipser, “Private Coins versus Public Coins in Interactive Proof Systems”, Proc. ISth Sym. on Theory of Computing (1986) pp. 59-68.
12. J. Hoperoft and J. Musinski, “Duality Applied to the Complexity of Matrix Multiplication and Other Bilinear Forms”, SIAM o r. Comput. 2 (1973), pp. 159-173.
13. Mark Jerrum, “A Compact Representation for Permutation Groups”, Journal of Algorithms 7 (1986), pp. 60-78.
14. Rodney W. Johnson and Aileen M. McLoughlin, “Noncommutative Bilinear Algorithms for 3 x 3 Matrix Multiplication”, SIAM J. Comput. 15 (1986), pp. 595-603.
15. Julian D. Laderman, “A Noncommutative Algorithm for Multiplying 3 x 3 Matrices Using 23 Multiplications”, Bull. Amer. Math. Soc. 82 (1976), pp. 126-128.
16. J. Leon, “Computing Automorphism Groups of Combinatorial Objects”, in Computational Group Theory, edited by M. D. Atkinson, Academic Press (1984), pp. 321-337.
17. E. M. Luks, “Isomorphisms of Graphs of Bounded Valence Can Be Tested in Polynomial Time”, J. Comp. Sys. Sci. 25 (1982), pp. 42-65.
18. Paul W. Purdom, “Tree Size by Partial Backtracking”, SIAM J. Comput. 7 (1978), pp. 481-491.
19. David A. Seaman, Faat Matriz Multiplication, Indiana University Master’s Thesis (1978).
20. C. C. Sims, “Computation with Permutation Groups”, in Proc. Second Sym. on Symbolic and Algebraic Manipulation, edited by S. R. Patrick, ACM, New York, 1971.
21. Votker Strassen, “Gaussian Elimination is Not Optimal”, Numer. Math. 13 (1969), pp. 354-356.