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Characteristics of the maximal independent set ZDD

Author

Listed:
  • David R. Morrison

    (Univerisity of Illinois, Urbana-Champaign)

  • Edward C. Sewell

    (Southern Illinois University, Edwardsville)

  • Sheldon H. Jacobson

    (Univerisity of Illinois, Urbana-Champaign)

Abstract

Zero-suppressed binary decision diagrams (ZDDs) are important data structures that are used in a number of combinatorial optimization settings. This paper explores a ZDD characterization for the maximal independent sets of a graph; a necessary and sufficient condition for when nodes in the ZDD can be merged is provided, and vertex orderings of the graph are studied to determine which orderings produce smaller ZDDs. A bound on the width of the maximal independent set ZDD is obtained, relating it to the Fibonacci numbers. Finally, computational results are reported.

Suggested Citation

  • David R. Morrison & Edward C. Sewell & Sheldon H. Jacobson, 2014. "Characteristics of the maximal independent set ZDD," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 121-139, July.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:1:d:10.1007_s10878-014-9722-4
    DOI: 10.1007/s10878-014-9722-4
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