Abstract
The exact minimization of the size of Ordered Binary Decision Diagrams (OBDD) is known to be an NP-complete problem. The available heuristical solutions of the problem still do not satisfy requirements of the practical applications. Development of the efficient algorithms that find acceptable variable orders within a short time and with a modest memory overhead is hence higly desired.
In this paper we contribute to the solution of the minimization problem by a new variable reordering heuristic that is based on sampling. A small OBDD sample is chosen from the OBDDs that are considered for minimization. Solving the problem for this small sample, we obtain a variable order that is extrapolated and applied to the entire OBDDs. We present the first experimental results with the Sample Reordering targeted at combinatorial verification. The suggested heuristic is substantially faster than Sifting.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
references
B. Bollig, M. Lobbig, and I. Wegener. Simulated Annealing to Improve Variable Orderings for OBDDs. Proc. IWLS, 5b:5-1–5-10, 1995.
J. Bern, Ch. Meinel, and A. Slobodova. Global Rebuilding of OBDDs-Avoiding Memory Requirement Maxima. Proc. CAV, (LNCS 939:299–308, 1995.
R.E. Bryant. Graph Based Algorithms for Boolean Function Manipulation. IEEE Transactions on Computers, (C-35):677–691, 1986.
B. Bollig and I. Wegener. Improving the Variable Ordering of OBDDs is NP-complete. IEEE Transactions on Computers, (45(9)):993–1002, 1996.
R. Drechsler, B. Becker, and N. Gockel. A Genetic Algorithm for Variable Ordering of OBDDs. IEEE Proc. Computers and Digital Techniques, 143(6):364–368, 1996.
R. Drechsler, N. Drechsler, and W. Günther. Fast Exact Minimization of BDDs. IEEE/ACM Proc. Design Automation Conference, 1998.
S.J. Friedman, and K.J. Supowit. Finding the Optimal Variable Ordering for Binary Decision Diagrams IEEE/ACM Proc. DAC, 348–356, 1987.
S.J. Friedman, and K.J. Supowit. Finding the Optimal Variable Ordering for Binary Decision Diagrams IEEE Transactions on Computers, 39(5):710–713, 1990.
N. Ishiura, H. Sawada, and S. Yajima. Minimization of Binary Decision Diagrams Based on Exchanges of Variables IEEE Proc. of ICC AD, 472–475, 1991.
Ch. Meinel and A. Slobodova. On the Complexity of Constructing Optimal Ordered Binary Decision Diagrams. Proc. MFCS, (LNCS 841):515–525, 1994.
Ch. Meinel and A. Slobodova. Speeding up Variable Reordering of OBDDs. IEEE Proc. of ICCD, 338–343, 1997.
S. Panda and F. Somenzi. Who are the Variables in Your Neighbourhood. Proc. ACM/IEEE ICCAD, 74–77, 1995.
S. Panda, F. Somenzi, and B.F. Plessier. Symmetry Detection and Dynamic Variable Ordering of Decision Diagrams. Proc. ICCAD, 628–631, 1994.
R. Rudell. Dynamic Variable Ordering for Ordered Binary Decision Diagrams. Proc. ACM/IEEE ICCAD, 42–47, 1993.
F. Somenzi. CUDD: CU Decision Diagram Package. Release 2.1.2. University of Colorado, Boulder) (ftp://vlsi.colorado.edu/pub/), 1997.
D. Sieling, and I. Wegener. Reduction of BDDs in Linear Time, Information Processing Letters, 48(3):139–144, 1993.
P. Savický, and I. Wegener. Efficient Algorithms for the Transformation Between Different Types of Binary Decision Diagrams Acta Informatica, 34:245–256, 1997.
S. Tani, K. Hamaguchi, and S. Yajima. The Complexity of the Optimal Variable Ordering Problem of Shared Binary Decision Diagrams. Proc. ISAAC, (LNCS762):389–398, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Slobodova, A., Meinel, C. (1998). Sample Method for Minimization of OBDDs. In: Rovan, B. (eds) SOFSEM’ 98: Theory and Practice of Informatics. SOFSEM 1998. Lecture Notes in Computer Science, vol 1521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49477-4_34
Download citation
DOI: https://doi.org/10.1007/3-540-49477-4_34
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65260-1
Online ISBN: 978-3-540-49477-5
eBook Packages: Springer Book Archive