Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Dynamic variable ordering for ordered binary decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
On-the-fly layout generation for PTL macrocells
Proceedings of the conference on Design, automation and test in Europe
The nonapproximability of OBDD minimization
Information and Computation
Memory-Bounded A* Graph Search
Proceedings of the Fifteenth International Florida Artificial Intelligence Research Society Conference
Multiple sequence alignment using anytime A*
Eighteenth national conference on Artificial intelligence
Quasi-Exact BDD Minimization Using Relaxed Best-First Search
ISVLSI '05 Proceedings of the IEEE Computer Society Annual Symposium on VLSI: New Frontiers in VLSI Design
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
BDS: a BDD-based logic optimization system
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Combining ordered best-first search with branch and bound for exact BDD minimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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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 so-called 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 is (1 + Ɛ)⌊N/2⌋ where 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 + Ɛ. The parameter Ɛ ≥ 0 can be chosen by the user. Within a range of reasonable choices for Ɛ, 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.