Efficient Algorithms for Listing Combinatorial Structures

Erscheinungsjahr 2012
ISBN: 978-0-521-45021-8
Verlag: Cambridge University Press

Buch, Englisch, Band 5, 176 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 497 g

Reihe: Distinguished Dissertations in Computer Science

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.

Autoren/Hrsg.

Goldberg, Leslie Ann

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Graphentheorie

Inhaltsverzeichnis

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.