Efficient Algorithms for Listing Combinatorial Structures

ISBN-13: 9780521450218 / Angielski / Twarda / 1993 / 178 str.

Peru) Leslie Ann Goldberg (Sandia National Laboratories

Opis

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.

Recenzje

"...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

Spis treści

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.