Chapter 2. Backtracking and Isomorph-Free Generation of Polyhexes
- Amiya Nayak B.Math., Ph.D. Adjunct Research Professor Associate Editor Full Professor2,
- Ivan Stojmenović Ph.D. Chair Professor founder editor-in-chief2,3
Published Online: 1 MAR 2007
DOI: 10.1002/9780470175668.ch2
Copyright © 2008 John Wiley & Sons, Inc.
Book Title
Handbook of Applied Algorithms: Solving Scientific, Engineering and Practical Problems
Additional Information
How to Cite
Moura, L. and Stojmenovic, I. (2007) Backtracking and Isomorph-Free Generation of Polyhexes, in Handbook of Applied Algorithms: Solving Scientific, Engineering and Practical Problems (eds A. Nayak and I. Stojmenović), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470175668.ch2
Editor Information
- 2
SITE, University of Ottawa, 800 King Edward Ave., Ottawa, ON K1N 6N5, Canada
- 3
EECE, University of Birmingham, UK
Publication History
- Published Online: 1 MAR 2007
- Published Print: 14 FEB 2008
ISBN Information
Print ISBN: 9780470044926
Online ISBN: 9780470175668
- Summary
- Chapter
Keywords:
- polyhexes - backtracking and isomorph-free generation;
- cage algorithm hexagonal system generation;
- hexagonal systems - perfect matchings
Summary
General combinatorial algorithms and their application to enumerating molecules in chemistry are presented and classical and new algorithms for the generation of complete lists of combinatorial objects that contain only inequivalent objects (isomorph-free exhaustive generation) are discussed. We introduce polygonal systems, and how polyhexes and hexagonal systems relate to benzenoid hydrocarbons. The central theme is the exhaustive generation of nonequivalent hexagonal systems, which is used to walk the reader through several algorithmic techniques of general applicability. The main algorithmic framework is backtracking, which is coupled with sophisticated methods for dealing with isomorphism or symmetries. Triangular and square systems, as well as the problem of matchings in hexagonal systems and their relationship to Kékule structures in chemistry are also presented.