Algorithms And Data Structures

Download e-book for iPad: Combinatorial Algorithms : An Update by Herbert S. Wilf

By Herbert S. Wilf

ISBN-10: 0898712319

ISBN-13: 9780898712315

This monograph is a survey of a few of the paintings that has been performed because the visual appeal of the second one variation of Combinatorial Algorithms. issues comprise development in: grey Codes, directory of subsets of given measurement of a given universe, directory rooted and loose bushes, identifying unfastened bushes and unlabeled graphs uniformly at random, and rating and unranking difficulties on unlabeled bushes.

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1-10. [Ba] L. BABAI, Long cycles in vertex-transitive graphs, J. Graph Theory, 3 (1979), pp. 301-304. [BER] JAMES R. BITNER, GIDEON EHRLICH, AND EDWARD M. , 19 (1976), pp. 517-521. [BH] TERRY BEYER AND SANDRA MITCHELL HEDETNIEMI, Constant time generation of rooted trees, SIAM J. , 9 (1980), pp. 706-712. [BW] M. BUCK AND D. , 48 (1984), pp. 19-29. [CLD] C. C. CHANG, R. C. T. LEE, AND M. W. Du, Symbolic Gray code as a perfect multiattribute hashing scheme for partial match queries, IEEE Trans. , 8 (1982), pp.

BER] JAMES R. BITNER, GIDEON EHRLICH, AND EDWARD M. , 19 (1976), pp. 517-521. [BH] TERRY BEYER AND SANDRA MITCHELL HEDETNIEMI, Constant time generation of rooted trees, SIAM J. , 9 (1980), pp. 706-712. [BW] M. BUCK AND D. , 48 (1984), pp. 19-29. [CLD] C. C. CHANG, R. C. T. LEE, AND M. W. Du, Symbolic Gray code as a perfect multiattribute hashing scheme for partial match queries, IEEE Trans. , 8 (1982), pp. 235249. [DW] JOHN D. DIXON AND HERBERT S. WILF, The random selection of unlabeled graphs, J.

We could carry out this analysis using the dihedral group of symmetries, but the cyclic group will be quite sufficient to show the ideas involved. A standard question in many combinatorics texts asks for the number of such necklaces, and it turns out to be where is Euler's function. The appearance of the "l/«" in front of this formula means that the sum by itself does overcounting that needs to be compensated for. Consequently, it will be hard to use the derivation of this formula as a model for an algorithm that would produce a list of all (n, k) necklaces.

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