Efficient Algorithms for Listing Combinatorial Structures

Leslie Ann Goldberg (Sandia National Laboratories, Peru)

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English

Cambridge University Press
30 July 2009

Combinatorics & graph theory; Algorithms & data structures

Series: Distinguished Dissertations in Computer Science

First published in 1993, this thesis is concerned with the design of efficient algorithms for listing combinatorial structures. The research described here gives some answers to the following questions: which families of combinatorial structures have fast computer algorithms for listing their members? What general methods are useful for listing combinatorial structures? How can these be applied to those families which are of interest to theoretical computer scientists and combinatorialists? Amongst those families considered are unlabelled graphs, first order one properties, Hamiltonian graphs, graphs with cliques of specified order, and k-colourable graphs. Some related work is also included, which compares the listing problem with the difficulty of solving the existence problem, the construction problem, the random sampling problem, and the counting problem. In particular, the difficulty of evaluating Pólya's cycle polynomial is demonstrated.

By: Leslie Ann Goldberg (Sandia National Laboratories Peru)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 5
Dimensions: Height: 244mm, Width: 170mm, Spine: 10mm
Weight: 300g
ISBN: 9780521117883
ISBN 10: 0521117887
Series: Distinguished Dissertations in Computer Science
Pages: 180
Publication Date: 30 July 2009
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Efficient Algorithms for Listing Combinatorial Structures

"""...selected as one of the three best theses in computer science in the UK in 1992....makes an important contribution to the complexity theory of listing and counting combinatorial structures....gives new and interesting results..."" Mathematical Reviews ""By any standard, this is an exceptional dissertation. It is well written, with the author always explaining the thrust of the argument, never allowing the technical nature of many of the results to obscure the overall picture. The author has built up a substantial theory...."" G.F. Royle, Computing Reviews ""...an impressive and thorough examination of listing problems in this framework...the complicated probabilistic arguments needed for the analysis are handled well...this is an exceptional dissertation...well-written, with the author always carefully explaining the thrust of the argument, never allowing the technical nature of many of the results to obscure the overall picture."" G.F. Royle, Mathematics of Computing"