Efficient Algorithms for Listing Combinatorial Structures
Published on 30. July 2009
Book
Paperback/Softback
180 pages
978-0-521-11788-3 (ISBN)
Description
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 Polya's cycle polynomial is demonstrated.
Reviews / Votes
"...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 ComputingMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 10 mm
Weight
322 gr
ISBN-13
978-0-521-11788-3 (9780521117883)
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Schweitzer Classification
Person
Content
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.