2. Backtracking and Isomorph-Free Generation of Polyhexes

  1. Amiya Nayak B.Math., Ph.D. Adjunct Research Professor Associate Editor Full Professor2 and
  2. Ivan Stojmenović Ph.D. Chair Professor founder editor-in-chief2,3
  1. Lucia Moura1 and
  2. Ivan Stojmenovic Ph.D. Chair Professor founder editor-in-chief2,3

Published Online: 1 MAR 2007

DOI: 10.1002/9780470175668.ch2

Handbook of Applied Algorithms: Solving Scientific, Engineering and Practical Problems

Handbook of Applied Algorithms: Solving Scientific, Engineering and Practical Problems

How to Cite

Moura, L. and Stojmenovic, I. (2008) 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

  1. 2

    SITE, University of Ottawa, 800 King Edward Ave., Ottawa, ON K1N 6N5, Canada

  2. 3

    EECE, University of Birmingham, UK

Author Information

  1. 1

    School of Information Technology and Engineering, University of Ottawa, Ottawa, ON K1N 6N5, Canada

  2. 2

    SITE, University of Ottawa, 800 King Edward Ave., Ottawa, ON K1N 6N5, Canada

  3. 3

    EECE, University of Birmingham, UK

Publication History

  1. Published Online: 1 MAR 2007
  2. Published Print: 14 FEB 2008

ISBN Information

Print ISBN: 9780470044926

Online ISBN: 9780470175668

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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.