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Variable orderings and the size of OBDDs for random partially symmetric Boolean functions
Author(s) -
Sieling Detlef
Publication year - 1998
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/(sici)1098-2418(199808)13:1<49::aid-rsa3>3.0.co;2-s
Subject(s) - mathematics , binary decision diagram , random variable , variable (mathematics) , boolean function , combinatorics , symmetric function , heuristic , discrete mathematics , binary number , algorithm , mathematical optimization , statistics , mathematical analysis , arithmetic
The size of ordered binary decision diagrams (OBDDs) strongly depends on the chosen variable ordering. It is an obvious heuristic to use symmetric variable orderings, i.e., variable orderings where symmetric variables are arranged adjacently. In order to evaluate this heuristic, methods for estimating the OBDD size for random partially symmetric functions are presented. Characterizations of cases where, with high probability, only symmetric variable orderings and, with high probability, only nonsymmetric variable orderings lead to minimum OBDD size are obtained. For this analysis estimates for the number of different blocks of random Boolean matrices are used. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13, 49–70, 1998