Solving Covering Problems Using LPR-based Lower Bounds

Liao, Stan; Devadas, Srinivas

doi:10.1109/dac.1997.597128

Cited by 34 publications

(55 citation statements)

References 9 publications

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“…In these cases we can guarantee that a better solution cannot be found with the current variable assignments and therefore the search can be pruned. The algorithms described in [5,12,20] follow this approach.…”

Section: Search Algorithms For Covering Problemsmentioning

confidence: 99%

“…Several lower bound estimation procedures can be used, namely the ones based on linear-programming relaxations [12], Lagrangian relaxations [16] or the Log-approximation approach [4]. Nevertheless, and for BCP, the approximation of a maximum independent set of clauses [4] is the most commonly used.…”

Section: Search Algorithms For Covering Problemsmentioning

confidence: 99%

“…Covering problems are often solved by branch-and-bound algorithms [5,12,20]. In these cases, each node of the search tree corresponds to a selected unassigned variable and the two branches out of the node represent the assignment of 1 and 0 to that variable.…”

Section: Preliminariesmentioning

confidence: 99%

“…(Details of the work on BCP can be found in [4,12,20].) Despite these improvements, and as with other NP-hard problems, additional search pruning ability allows in general very significant gains, both in the amount of search and in the run times.…”

Section: Introductionmentioning

confidence: 99%

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Satisfiability-Based Algorithms for Boolean Optimization

Manquinho

Marques-Silva

2004

Annals of Mathematics and Artificial Intelligence

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Abstract.This paper proposes new algorithms for the Binate Covering Problem (BCP), a well-known restriction of Boolean Optimization. Binate Covering finds application in many areas of Computer Science and Engineering. In Artificial Intelligence, BCP can be used for computing minimum-size prime implicants of Boolean functions, of interest in Automated Reasoning and Non-Monotonic Reasoning. Moreover, Binate Covering is an essential modeling tool in Electronic Design Automation. The objectives of the paper are to briefly review branch-and-bound algorithms for BCP, to describe how to apply backtrack search pruning techniques from the Boolean Satisfiability (SAT) domain to BCP, and to illustrate how to strengthen those pruning techniques by exploiting the actual formulation of BCP. Experimental results, obtained on representative instances indicate that the proposed techniques provide significant performance gains for a large number of problem instances.

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Section: Search Algorithms For Covering Problemsmentioning

confidence: 99%

Section: Search Algorithms For Covering Problemsmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Satisfiability-Based Algorithms for Boolean Optimization

Manquinho

Marques-Silva

2004

Annals of Mathematics and Artificial Intelligence

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“…Exact solutions are proposed in [54,55]. Clearly a method is efficient if it is possible to prevent the exploration of unsuccessful branches at earlier stages of the search, and this relies on efficient bounding techniques [38,39,56,57].…”

Section: Instruction Selectionmentioning

confidence: 99%

The Instruction-Set Extension Problem: A Survey

Galuzzi

Bertels

Lecture Notes in Computer Science

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Abstract.Over the last years, we have witnessed the increased use of Application-Specific Instruction-Set Processors (ASIPs). These ASIPs are processors that have a customizable instruction-set, which can be tuned towards specific requirements. The identification, definition and implementation of those operations that provide the largest performance improvement and that should be hardwired, extending in this way the Instruction-Set, constitutes a major challenge. The purpose of this paper is to investigate and study the issues regarding the customization of an Instruction-Set in function of the specific requirements of an application. Additionally, the paper provides an overview of all relevant aspects of the problem and compensates the lack of a general view of the problem in the existing literature.

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On Applying Cutting Planes in DLL-Based Algorithms for Pseudo-Boolean Optimization

Manquinho

Marques-Silva

2005

Theory and Applications of Satisfiability Testing

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Abstract. The utilization of cutting planes is a key technique in Integer Linear Programming (ILP). However, cutting planes have seldom been applied in Pseudo-Boolean Optimization (PBO) algorithms derived from the Davis-Logemann-Loveland (DLL) procedure for Propositional Satisfiability (SAT). This paper proposes the utilization of cutting planes in a DLL-style PBO algorithm, which incorporates the most effective techniques for PBO. We propose the utilization of cutting planes both during preprocessing and during the search process. Moreover, we also establish conditions that enable clause learning and non-chronological backtracking in the presence of conflicts involving constraints generated by cutting plane techniques. The experimental results, obtained on a large number of classes of instances, indicate that the integration of cutting planes with backtrack search is an extremely effective technique for PBO.

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Solving Covering Problems Using LPR-based Lower Bounds

Cited by 34 publications

References 9 publications

Satisfiability-Based Algorithms for Boolean Optimization

Satisfiability-Based Algorithms for Boolean Optimization

The Instruction-Set Extension Problem: A Survey

On Applying Cutting Planes in DLL-Based Algorithms for Pseudo-Boolean Optimization

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