Detecting embedded Horn structure in propositional logic

Chandru, V.; Hooker, John

doi:10.1016/0020-0190(92)90098-g

Cited by 15 publications

(9 citation statements)

References 6 publications

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“…One type of experimental design ( a "factorial design") begins with a list of n factors that could affect performance--perhaps problem size, density, existence of a solution, closeness to "renamable Horn" (Aspvall, 1980;Chandru et al, 1990;Chandru and Hooker, 1992), and so on. Each factor i has several levels k i = 1 ..... mi, corresponding to different problem sizes, densities, and so on.…”

Section: A More Scientific Alternativementioning

confidence: 99%

Testing heuristics: We have it all wrong

1995

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The competitive nature of most algorithmic experimentation is a source of problems that are all too familiar to the research community. It is hard to make fair comparisons between algorithms and to assemble realistic test problems. Competitive testing tells us which algorithm is faster but not why. Because it requires polished code, it consumes time and energy that could be better spent doing more experiments. This article argues that a more scientific approach of controlled experimentation, similar to that used in other empirical sciences, avoids or alleviates these problems. We have confused research and development; competitive testing is suited only for the latter.Key Words: computational testing, benchmark problems Most experimental studies of heuristic algorithms resemble track meets more than scientific endeavors.Typically an investigator has a bright idea for a new algorithm and wants to show that it works better, in some sense, than known algorithms. This requires computational tests, perhaps on a standard set of benchmark problems. If the new algorithm wins, the work is submitted for publication. Otherwise it is written off as a failure. In short, the whole affair is organized around an algorithmic race whose outcome determines the fame and fate of the contestants.This modus operandi spawns a host of evils that have become depressingly familiar to the algorithmic research community. They are so many and pervasive that even a brief summary requires an entire section of this article. Two, however, are particularly insidious. The emphasis on competition is fundamentally anti-intellectual and does not build the sort of insight that in the long run is conducive to more effective algorithms. It tells us which algorithms are better but not why. The understanding we do accrue generally derives from initial tinkering that takes place in the design stages of the algorithm. Because only the results of the formal competition are exposed to the fight of publication, the observations that are richest in information are too often conducted in an informal, uncontrolled manner. Second, competition diverts time and resources from productive investigation. Countless hours are spent crafting the fastest possible code and finding the best possible parameter settings in order to obtain results that are suitable for publication. This is particularly unfortunate because it squanders a natural advantage of empirical algorithmic work. Most empirical work in other sciences tends to be slow and expensive, requiring well-appointed laboratories, massive equipment, or carefully selected subjects. By contrast, much empirical work on algorithms can be carried out on a work station by a single investigator. This advantage should be exploited by conducting more experiments, rather than by implementing each one in the fastest possible code.

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Section: A More Scientific Alternativementioning

confidence: 99%

Testing heuristics: We have it all wrong

1995

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“…Variable deletion has been recently investigated by Chandru and Hooker [6] and Truemper [14]. Although this operation is not really of an "algebraic" nature, it plays an interesting role in the study of control sets, mostly because of its close relationship with variable fixation.…”

Section: Removing Variables or Terms From Dnfsmentioning

confidence: 99%

“…The notion of control set has been exploited by numerous researchers either to decompose an original, hard problem into a collection of simpler ones, or to approximate the original problem by a simpler one (see e.g. 2,[4][5][6][7]. In most of these investigations a central issue is then to identify control sets of small cardinality.…”

Section: Introductionmentioning

confidence: 99%

Variable and term removal from Boolean formulae

Crama

Ekin

Hammer

1997

Discrete Applied Mathematics

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Given a Boolean formula in disjunctive normal form, the variable deletion control set problem consists in finding a minimum cardinality set of variables whose deletion from the formula results in a DNF satisfying some prescribed property. Similar problems can be defined with respect to the fixation of variables or the deletion of terms in a DNF. In this paper, we investigate the complexity of such problems for a broad class of DNF properties.

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“…For instance, a subproblem in which the clauses are renamable Horn can be checked for satisfiability in linear time [1,10]. Finding a small subset of variables y for which the subproblem is always renamable Horn is a maximum clique problem [11], which can be solved by various heuristics and exact algorithms.…”

Section: Propositional Satisfiabilitymentioning

confidence: 99%

“…provided either (11) or (12) is feasible. If the dual (12) has a finite solution u, then u provides an inference procedure (a linear combination) for obtaining a valid bound on the objective function value z of (10):…”

Section: Classical Benders Decompositionmentioning

confidence: 99%

Logic-based Benders decomposition

Hooker¹,

Ottosson²

2003

Math. Program., Ser. A

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403

260

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Benders decomposition uses a strategy of "learning from one's mistakes." The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an "inference dual." Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different from other generalized duals that have been proposed. The approach is illustrated by working out the details for propositional satisfiability and 0-1 programming problems. Computational tests are carried out for the latter, but the most promising contribution of logic-based Benders may be to provide a framework for combining optimization and constraint programming methods. *

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Detecting embedded Horn structure in propositional logic

Cited by 15 publications

References 6 publications

Testing heuristics: We have it all wrong

Testing heuristics: We have it all wrong

Variable and term removal from Boolean formulae

Logic-based Benders decomposition

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