Optimal speedup of Las Vegas algorithms

Luby, Michael; Sinclair, Alistair; Zuckerman, David

doi:10.1016/0020-0190(93)90029-9

Cited by 377 publications

(327 citation statements)

References 2 publications

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“…Modern SAT solvers based on the CDCL paradigm restart often by frequently backtracking to the root-level (also called top-level) [27,28,29,30] using a specific restart schedule [31,32,33,34]. With assumptions it seems however to be more natural to backtrack to the highest decision level, where the last assumption was assigned, which we call assumption-level.…”

Section: Factoring Out Assumptionsmentioning

confidence: 99%

Factoring Out Assumptions to Speed Up MUS Extraction

Lagniez

Biere

2013

Lecture Notes in Computer Science

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Abstract. In earlier work on a limited form of extended resolution for CDCL based SAT solving, new literals were introduced to factor out parts of learned clauses. The main goal was to shorten clauses, reduce proof size and memory usage and thus speed up propagation and conflict analysis. Even though some reduction was achieved, the effectiveness of this technique was rather modest for generic SAT solving. In this paper we show that factoring out literals is particularly useful for incremental SAT solving, based on assumptions. This is the most common approach for incremental SAT solving and was pioneered by the authors of MINISAT. Our first contribution is to focus on factoring out only assumptions, and actually all eagerly. This enables the use of compact dedicated data structures, and naturally suggests a new form of clause minimization, our second contribution. As last main contribution, we propose to use these data structures to maintain a partial proof trace for learned clauses with assumptions, which gives us a cheap way to flush useless learned clauses. In order to evaluate the effectiveness of our techniques we implemented them within the version of MINISAT used in the publically available state-of-the-art MUS extractor MUSer. An extensive experimental evaluation shows that factoring out assumptions in combination with our novel clause minimization procedure and eager clause removal is particularly effective in reducing average clause size, improves running time and in general the state-of-the-art in MUS extraction.

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Section: Factoring Out Assumptionsmentioning

confidence: 99%

Factoring Out Assumptions to Speed Up MUS Extraction

Lagniez

Biere

2013

Lecture Notes in Computer Science

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“…In [3] it is further shown that the expected run time of LUBY(x) is within a logarithmic factor from the expected run time of OPTIMUM(x) independently of x. -WALSH.…”

Section: Fig 2 Run Time Distributions and Expected Run Times For Thmentioning

confidence: 99%

“…for a given RSP and instance x [3]. If the cumulative distribution function q(t) of the instance is known, the optimal restart limit t * may be determined by minimizing the expected run time E(T FIXED t(x) ) as a function of the restart limit t,…”

Section: Fig 2 Run Time Distributions and Expected Run Times For Thmentioning

confidence: 99%

“…and the algorithm corresponding to the fixed restart strategy S t employed on RSP is denoted by FIXED t,RSP (or simply FIXED t when RSP is implicitly known). Fixed restart strategies are important in our analysis, since if q RSP(x) (t) is known, then t can be chosen so that the expected run time of FIXED t (x) is the minimal among all the algorithms obtainable from RSP(x) by employing any restart strategy [3]. However, in practice q RSP(x) (t) is not known: obtaining information about q RSP(x) (t) in general requires solving RSP(x), which is the overall goal in many applications.…”

Section: Introductionmentioning

confidence: 99%

“…However, in practice q RSP(x) (t) is not known: obtaining information about q RSP(x) (t) in general requires solving RSP(x), which is the overall goal in many applications. To circumvent this problem, several universal restart strategies have been suggested [3,4]: they do not depend on the instance x and let the restart limits grow arbitrary large in order to preserve the completeness of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Strategies for Solving SAT in Grids by Randomized Search

Hyvärinen¹,

Junttila²,

Niemelä³

Lecture Notes in Computer Science

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Abstract. Grid computing offers a promising approach to solving challenging computational problems in an environment consisting of a large number of easily accessible resources. In this paper we develop strategies for solving collections of hard instances of the propositional satisfiability problem (SAT) with a randomized SAT solver run in a Grid. We study alternative strategies by using a simulation framework which is composed of (i) a grid model capturing the communication and management delays, and (ii) run-time distributions of a randomized solver, obtained by running a state-of-the-art SAT solver on a collection of hard instances. The results are experimentally validated in a production level Grid. When solving a single hard SAT instance, the results show that in practice only a relatively small amount of parallelism can be efficiently used; the speedup obtained by increasing parallelism thereafter is negligible. This observation leads to a novel strategy of using grid to solve collections of hard instances. Instead of solving instances one-by-one, the strategy aims at decreasing the overall solution time by applying an alternating distribution schedule.

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How to couple from the past using a read-once source of randomness

Wilson¹

2000

Random Struct. Alg.

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We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related to an idea known as PASTA (Poisson arrivals see time averages) in the operations research literature. Because the new algorithm can be run using a read-once stream of randomness, we call it read-once CFTP. The memory and time requirements of read-once CFTP are on par with the requirements of the usual form of CFTP, and for a variety of applications the requirements may be noticeably less. Some perfect sampling algorithms for point processes are based on an extension of CFTP known as coupling into and from the past; for completeness, we give a read-once version of coupling into and from the past, but it remains unpractical. For these point process applications, we give an alternative coupling method with which read-once CFTP may be efficiently used.

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Optimal speedup of Las Vegas algorithms

Cited by 377 publications

References 2 publications

Factoring Out Assumptions to Speed Up MUS Extraction

Factoring Out Assumptions to Speed Up MUS Extraction

Strategies for Solving SAT in Grids by Randomized Search

How to couple from the past using a read-once source of randomness

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