Efficient Algorithms for Listing Combinatorial Structures

by Leslie Ann Goldberg

Overview

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 that are of interest to theoretical computer scientists and combinatorialists? Among those families considered are unlabeled graphs, first-order one properties, Hamiltonian graphs, graphs with cliques of specified order, and k-colorable graphs. Some related work is also included that 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 Polya's cycle polynomial is demonstrated.

Product Details

ISBN-13:	9780521450218
Publisher:	Cambridge University Press
Publication date:	04/22/1993
Series:	Distinguished Dissertations in Computer Science , #5
Edition description:	A Ph.D. dissertation
Pages:	178
Product dimensions:	6.69(w) x 9.61(h) x 0.43(d)

Table of Contents

1. Introduction; 2. Techniques for listing combinatorial structures; 3. Applications to particular families of structures; 4. Directions for future work on listing; 5. Related results; 6. Bibliography.

Editorial Reviews

"...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

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