1. Generating All and Random Instances of a Combinatorial Object

  1. Amiya Nayak B.Math., Ph.D. Adjunct Research Professor Associate Editor Full Professor1 and
  2. Ivan Stojmenović Ph.D. Chair Professor founder editor-in-chief1,2
  1. Ivan Stojmenovic Ph.D. Chair Professor founder1,2

Published Online: 1 MAR 2007

DOI: 10.1002/9780470175668.ch1

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

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

How to Cite

Stojmenovic, I. (2007) Generating All and Random Instances of a Combinatorial Object, 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.ch1

Editor Information

  1. 1

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

  2. 2

    EECE, University of Birmingham, UK

Author Information

  1. 1

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

  2. 2

    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

SEARCH

Keywords:

  • combinatorial object - generating all and random instances;
  • listing combinations and permutations;
  • combinatorial objects - ranking and unranking

Summary

Many practical problems require an exhaustive search through the solution space, which are represented as combinatorial structures, such as, permutations, combinations, set partitions, integer partitions, and trees. All combinatorial objects of a certain kind need to be generated to test all possible solutions. In some other problems, a randomly generated object is needed, or an object with an approximately correct ranking among all objects, without using large integers. Fast algorithms for generating all objects, random object, or object with approximate ranking for basic types of combinatorial objects are described.