The Theory of Zero-Suppressed BDDs and the Number of Knight‘s Tours

  • Authors:
  • Olaf Schröer;Ingo Wegener

  • Affiliations:
  • FB Informatik, LS II, Univ. Dortmund, 44221 Dortmund, Germany;FB Informatik, LS II, Univ. Dortmund, 44221 Dortmund, Germany. Email: wegener@ls2.informatik.uni-dortmund.de

  • Venue:
  • Formal Methods in System Design
  • Year:
  • 1998

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Abstract

Zero-suppressed binary decision diagrams (ZBDDs)have been introduced by Minato [14–17] who presents applications for cubeset representations, fault simulation, timing analysis and the n-queens problem. Here the structural properties of ZBDDs areworked out and a generic synthesis algorithm is presented andanalyzed. It is proved that ZBDDs can be at most by a factorn + 1smaller or larger than ordered BDDs (OBDDs) for the same functionon n variables. Using ZBDDs the best known upper bound on thenumber of knight‘s tours on an 8 × 8 chessboard is improvedsignificantly.