Cost-optimal constrained correlation clustering via weighted partial Maximum Satisfiability

Berg, Jeremias; Järvisalo, Matti

doi:10.1016/j.artint.2015.07.001

Cited by 24 publications

(23 citation statements)

References 75 publications

(150 reference statements)

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“…Maximum satisfiability (MaxSAT), the optimization variant of Boolean satisfiability (SAT), provides a competitive approach to various real-world optimization problems arising from AI and industrial applications, see e.g. [18,34,25,14,33,7,6]. Most of the modern MaxSAT solvers are based on iteratively transforming an input problem instance in specific ways towards a representation from which an optimal solution is in some sense "easy" to compute.…”

Section: Introductionmentioning

confidence: 99%

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

Berg

Järvisalo

2019

Logics in Artificial Intelligence

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A central algorithmic paradigm in maximum satisfiability solving geared towards real-world optimization problems is the coreguided approach. Furthermore, recent progress on preprocessing techniques is bringing in additional reasoning techniques to MaxSAT solving. Towards realizing their combined potential, understanding formal underpinnings of interleavings of preprocessing-style reasoning and core-guided algorithms is important. It turns out that earlier proposed notions for establishing correctness of core-guided algorithms and preprocessing, respectively, are not enough for capturing correctness of interleavings of the techniques. We provide an in-depth analysis of these and related MaxSAT instance transformations, and propose correction set reducibility as a notion that captures inprocessing MaxSAT solving within a state-transition style abstract MaxSAT solving framework. Furthermore, we establish a general theorem of correctness for applications of SAT-based preprocessing techniques in MaxSAT. The results pave way for generic techniques for arguing about the formal correctness of MaxSAT algorithms.

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Section: Introductionmentioning

confidence: 99%

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

Berg

Järvisalo

2019

Logics in Artificial Intelligence

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“…, v n denote the binary optimization variables, and S + j /S − j denotes the set of variables and negated variables respectively in the jth clause. MAXSAT problems have been used to solve probabilistic inference (Park, 2002), planning (Zhang and Bacchus, 2012), and clustering (Berg and Järvisalo, 2017). And the recent MAXSAT contests (Argelich et al, 2016) have aimed at evaluating a wide number of different solution methods on a wide variety of both real and synthetic problems.…”

Section: Introductionmentioning

confidence: 99%

Low-Rank Semidefinite Programming for the MAX2SAT Problem

Wang

Kolter

2019

AAAI

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This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.

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“…Building on the extraordinary success of SAT solvers, exact solvers for MaxSAT-and, especially, its weighted partial generalization-are finding an increasing number of applications, ranging e.g. from hardware design debugging and modelbased diagnosis to bioinformatics and data analysis [4], [5], [6], [7], [8], [9], [10], [11]. This is brought on by recent improvements in MaxSAT solving techniques [12], [13], [14], [15], [2], [16], [3], [17], [18].…”

Section: Introductionmentioning

confidence: 99%

Re-using Auxiliary Variables for MaxSAT Preprocessing

Berg

Saikko

Järvisalo

2015

2015 IEEE 27th International Conference on Tools With Artificial Intelligence (ICTAI)

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Solvers for the maximum satisfiability (MaxSAT) problem-a well-known optimization variant of Boolean satisfiability (SAT)-are finding an increasing number of applications. Preprocessing has proven an integral part of the SATbased approach to efficiently solving various types of real-world problem instances. It was recently shown that SAT preprocessing for MaxSAT becomes more effective by re-using the auxiliary variables introduced in the preprocessing phase directly in the SAT solver within a core-based hybrid MaxSAT solver. We take this idea of re-using auxiliary variables further by identifying them among variables already present in the input MaxSAT instance. Such variables can be re-used already in the preprocessing step, avoiding the introduction of multiple layers of new auxiliary variables in the process. Empirical results show that by detecting auxiliary variables in the input MaxSAT instances can lead to modest additional runtime improvements when applied before preprocessing. Furthermore, we show that by re-using auxiliary variables not only within preprocessing but also as assumptions within the SAT solver of the MaxHS MaxSAT algorithm can alone lead to performance improvements similar to those observed by applying SAT-based preprocessing.

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Cost-optimal constrained correlation clustering via weighted partial Maximum Satisfiability

Cited by 24 publications

References 75 publications

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

Low-Rank Semidefinite Programming for the MAX2SAT Problem

Re-using Auxiliary Variables for MaxSAT Preprocessing

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