Improving the variable ordering of OBDDs is NP-complete

Bollig, Beate; Wegener, Ingo

doi:10.1109/12.537122

Cited by 437 publications

(242 citation statements)

References 17 publications

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“…This reduction of decision nodes directly affects the size of the BDD representation and the time cost of BDD operations. To find an optimal variable ordering for constructing a minimum-size BDD is known to be an NP-complete problem [2]. As a consequence, using heuristic to construct a near optimal reduced ordered BDD is crucial for achieving good performance in BDD-based operations.…”

Section: Binary Decision Diagrammentioning

confidence: 99%

Improving BDD-based attractor detection for synchronous Boolean networks

Yuan

Pang

et al. 2016

Sci. China Inf. Sci.

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Boolean networks are an important formalism for modelling biological systems and have attracted much attention in recent years. An important direction in Boolean networks is to exhaustively find attractors, which represent steady states when a biological network evolves for a long term. In this paper, we propose a new approach to improve the efficiency of BDD-based attractor detection. Our approach includes a monolithic algorithm for small networks, an enumerative strategy to deal with large networks, and two heuristics on ordering BDD variables. We demonstrate the performance of our approach on a number of examples, and compare it with one existing technique in the literature.

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Section: Binary Decision Diagrammentioning

confidence: 99%

Improving BDD-based attractor detection for synchronous Boolean networks

Yuan

Pang

et al. 2016

Sci. China Inf. Sci.

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“…the size of a BDD (measured in the number ofnodes) may vary from linear to exponential. Finding the optimal variable ordering is an NP-hard problem [Bollig and Wegener, 1996] and the best known algorithms have exponential worst case runtime [Friedman andSupowit, 1987, Drechsler et al, 1998]. …”

Section: Introductionmentioning

confidence: 99%

History-Based Dynamic Minimization During BDD Construction

Drechsler¹,

Günther²

2000

VLSI: Systems on a Chip

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Binary Decision Diagrams (BDDs) are the state-of-the-art data structure in VLSI CAD. Since their size largely depends on the chosen variable ordering, dynamic variable reordering methods, like sifting, often have to be applied while the BDD for a given circuit is constructed. Usually sifting is called each time a given node limit is reached and it is therefore called frequently during the construction of large BDDs. Often most of the runtime is spent for sifting while the BDD is built. In this paper we propose an approach to reduce runtime (and space requirement) during BDD construction by using history-based decision procedures. Dependent on the history of the construction process different types of sifting are called. We propose two methods that consider the quality of the hash table and the size reduction of previous sifting runs, respectively. Experimental results show that both approaches reduce the runtime significantly, i.e. by more than 40% on average.

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“…It has been shown that it is NP-complete to decide whether the number of nodes of a given BDD can be improved by variable reordering [1]. Moreover, the existence of a polynomial algorithm to approximate the optimal variable ordering of BDDs implies P = NP [12].…”

Section: Resultsmentioning

confidence: 99%

“…In brief, the result states that the choice of the next node to expand as performed by A * DW and A * ↑ conforms to the relaxation strategy of A * as stated in Equation (1). Notice that, despite the fact that A * DW and A * ↑ are formulated by use of evaluation functions that are different from that of A * or A * (i.e., different from ϕ = g + h), they provably act as if ϕ = g + h would be used.…”

Section: Proof See the Appendixmentioning

confidence: 99%

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A Framework for Quasi-exact Optimization Using Relaxed Best-First Search

Ebendt

Drechsler

Lecture Notes in Computer Science

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Abstract. In this paper, a framework for previous and new quasi-exact extensions of the A * -algorithm is presented. In contrast to previous approaches, the new methods guarantee to expand every state at most once if guided by a socalled monotone heuristic. By that, they account more effectively for aspects of run time while still guaranteeing that the cost of the solution will not exceed the optimal cost by a certain factor. First a general upper bound for this factor is derived. This bound iswhere N is (an upper bound on) the maximum depth of the search. Next, we look at specific instances of the algorithm class described by our framework. For one of the new methods a linear, i.e. much tighter upper bound is obtained: the cost of the solution will not exceed the optimal cost by a factor greater than 1 + . The parameter ≥ 0 can be chosen by the user. Within a range of reasonable choices for , all new methods allow the user to trade off run time for solution quality. Besides that, the formal framework also serves for a comparison in terms of other algorithmic properties of interest, e.g. in terms of a necessary condition for state expansion. The results of experiments targeting the minimization of Binary Decision Diagrams (BDDs) demonstrate large reductions in run time when compared to the best known exact approach for BDD minimization and to previous relaxation methods. Moreover, the quality of the obtained solutions is often much better than the quality guaranteed by the theory.

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Improving the variable ordering of OBDDs is NP-complete

Cited by 437 publications

References 17 publications

Improving BDD-based attractor detection for synchronous Boolean networks

Improving BDD-based attractor detection for synchronous Boolean networks

History-Based Dynamic Minimization During BDD Construction

A Framework for Quasi-exact Optimization Using Relaxed Best-First Search

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