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Improving the Variable Ordering of OBDDs Is NP-Complete
September 1996 (vol. 45 no. 9)
pp. 993-1002

Abstract—Ordered binary decision diagrams are a useful representation of Boolean functions, if a good variable ordering is known. Variable orderings are computed by heuristic algorithms and then improved with local search and simulated annealing algorithms. This approach is based on the conjecture that the following problem is NP-complete. Given an OBDD G representing f and a size bound s, does there exist an OBDD G* (respecting an arbitrary variable ordering) representing f with at most s nodes? This conjecture is proved.

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Index Terms:
Ordered binary decision diagrams, NP-completeness, variable orderings, verification, graph algorithms.
Beate Bollig, Ingo Wegener, "Improving the Variable Ordering of OBDDs Is NP-Complete," IEEE Transactions on Computers, vol. 45, no. 9, pp. 993-1002, Sept. 1996, doi:10.1109/12.537122
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