Some new combinatorial algorithms with appropriate representations of solutions
Main Article Content
Abstract
Abstract. Combinatorial problems are those problems, whose requirements are an association of some conditions. The construction of efficient algorithms to find solutions of the combinatorial problems is still an interesting matter. In this paper, we choose appropriate representations for desirable solutions of the permutation problem and the partition problem. Then we sort the representations of a problem's solutions in the alphabetical order. Owing to it we construct two new algorithms for quickly finding all solutions of these problems.
References
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[2] J. Ginsburg, Determining a permutation from its set of reductions, Ars Combinatoria, No. 82, 2007, pp. 55-57.
[3] T. Kuo, A new method for generating permutations in lexicographic order, Journal of Science and Engineering Technology, Vol. 5, No. 4, 2009, pp. 21-20.
[4] M. Monks, Reconstructing permutations from cycle minors, The Electronic Journal of Combinatorics, No. 16, 2009, #R19.
[5] W. Lipski, Kombinatoryka dla programistów, WNT, Warszawa, 1982.
[6] H.C. Thanh, Combinatorics, VNUH Press, 1999 (in Vietnamese).
[7] H.C. Thanh, Bounded sequence problem and some its applications, Proceedings of Japan-Vietnam Workshop on Software Engineering, Hanoi - 2010, pp. 74-83.
[8] H.C. Thanh, N.T.T. Loan, N.D. Ham, From Permutations to Iterative Permutations, International Journal of Computer Science Engineering and Technology, Vol. 2, Issue 7, 2012, pp. 1310-1315.