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  3. Efficient Algorithms for Listing Combinatorial Structures
  • Cited by 38
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
1993
Online ISBN:
9780511569913
DOI:
https://doi.org/10.1017/CBO9780511569913
Subjects:
Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Distributed, Networked and Mobile Computing, Computing: General Interest
Series:
Distinguished Dissertations in Computer Science (5)
Information

Book 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 Pólya's cycle polynomial is demonstrated.

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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