Jeremias Berg

LMHS: A SAT-IP Hybrid MaxSAT Solver

We describe LMHS, an open-source weighted partial maximum satisfiability (MaxSAT) solver. LMHS is a hybrid SAT-IP MaxSAT solver that implements the implicit hitting set approach to MaxSAT. On top of the main algorithm, LMHS offers integrated preprocessing, solution enumeration, an incremental API, and the use of a choice of SAT and IP solvers. We describe the main features of LMHS, and give empirical results on the influence of preprocessing and the choice of the underlying SAT and IP solvers on the performance of LMHS.

SAT-Based Approaches to Treewidth Computation: An Evaluation

Tree width is an important structural property of graphs, tightly connected to computational tractability in eg various constraint satisfaction formalisms such as constraint programming, Boolean satisfiability, and answer set programming, as well as probabilistic inference, for instance. An obstacle to harnessing tree width as a way to efficiently solving bounded tree width instances of NP-hard problems is that deciding tree width, and hence computing an optimal tree-decomposition, is in itself an NP-complete problem. In this paper, we study the applicability of Boolean satisfiability (SAT) based approaches to determining the tree widths of graphs, and at the same time obtaining an associated optimal tree-decomposition. Extending earlier studies, we evaluate various SAT and Max SAT based strategies for tree width computation, and compare these approaches to practical dedicated exact algorithms for the problem.

Optimal Correlation Clustering via MaxSAT

We introduce an extensible framework for correlation clustering by harnessing the Maximum satisfiability (MaxSAT) Boolean optimization paradigm. The approach is based on formulating the correlation clustering task in an exact fashion as MaxSAT, and then using a state-of-the-art MaxSAT solver for finding clusterings by solving the MaxSAT formulation. Our approach allows for finding optimal clusterings wrt the objective function of the problem, extends to constrained correlation clustering-by allowing for easy integration of user-defined domain knowledge in terms of hard constraints over the clusterings of interest-as well as overlapping correlation clustering. First experiments on the scalability of the approach are presented.

Cost-optimal constrained correlation clustering via weighted partial Maximum Satisfiability

Abstract Integration of the fields of constraint solving and data mining and machine learning has recently been identified within the AI community as an important research direction with high potential. This work contributes to this direction by providing a first study on the applicability of state-of-the-art Boolean optimization procedures to cost-optimal correlation clustering under constraints in a general similarity-based setting. We develop exact formulations of the correlation clustering task as Maximum Satisfiability (MaxSAT), the optimization version of the Boolean satisfiability (SAT) problem. For obtaining cost-optimal clusterings, we apply a state-of-the-art MaxSAT solver for solving the resulting MaxSAT instances optimally, resulting in cost-optimal clusterings. We experimentally evaluate the MaxSAT-based approaches to cost-optimal correlation clustering, both on the scalability of our method and the quality of the clusterings obtained. Furthermore, we show how the approach extends to constrained correlation clustering, where additional user knowledge is imposed as constraints on the optimal clusterings of interest. We show experimentally that added user knowledge allows clustering larger datasets, and at the same time tends to decrease the running time of our approach. We also investigate the effects of MaxSAT-level preprocessing, symmetry breaking, and the choice of the MaxSAT solver on the efficiency of the approach.

Re-using Auxiliary Variables for MaxSAT Preprocessing

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 SAT-based 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.

Subsumed Label Elimination for Maximum Satisfiability

We propose subsumed label elimination (SLE), a socalled label-based preprocessing technique for the Boolean optimization paradigm of maximum satisfiability (MaxSAT). We formally show that SLE is orthogonal to previously proposed SAT-based preprocessing techniques for MaxSAT in that it can simplify the underlying minimal unsatisfiable core structure of MaxSAT instances. We also formally show that SLE can considerably reduce the number of internal SAT solver calls within modern core-guided MaxSAT solvers. Empirically, we show that combining SLE with SAT-based preprocessing improves the performance of various state-of-the-art MaxSAT solvers on standard industrial weighted partial MaxSAT benchmarks.

MaxPre: An Extended MaxSAT Preprocessor

We describe MaxPre, an open-source preprocessor for (weighted partial) maximum satisfiability (MaxSAT). MaxPre implements both SAT-based and MaxSAT-specific preprocessing techniques, and offers solution reconstruction, cardinality constraint encoding, and an API for tight integration into SAT-based MaxSAT solvers.

Minimum-Width Confidence Bands via Constraint Optimization

The use of constraint optimization has recently proven to be a successful approach to providing solutions to various NP-hard search and optimization problems in data analysis. In this work we extend the use of constraint optimization systems further within data analysis to a central problem arising from the analysis of multivariate data, namely, determining minimum-width multivariate confidence intervals, i.e., the minimum-width confidence band problem (MWCB). Pointing out drawbacks in recently proposed formalizations of variants of MWCB, we propose a new problem formalization which generalizes the earlier formulations and allows for circumvention of their drawbacks. We present two constraint models for the new problem in terms of mixed integer programming and maximum satisfiability, as well as a greedy approach. Furthermore, we empirically evaluate the scalability of the constraint optimization approaches and solution quality compared to the greedy approach on real-world datasets.

Weight-Aware Core Extraction in SAT-Based MaxSAT Solving.

Maximum satisfiability (MaxSAT) is today a competitive approach to tackling NP-hard optimization problems in a variety of AI and industrial domains. A great majority of the modern state-of-the-art MaxSAT solvers are core-guided, relying on a SAT solver to iteratively extract unsatisfiable cores of the soft clauses in the working formula and ruling out the found cores via adding cardinality constraints into the working formula until a solution is found. In this work we propose weight-aware core extraction (WCE) as a refinement to the current common approach of core-guided solvers. WCE integrates knowledge of soft clause weights into the core extraction process, and allows for delaying the addition of cardinality constraints into the working formula. We show that WCE noticeably improves in practice the performance of PMRES, one of the recent core-guided MaxSAT algorithms using soft cardinality constraints, and explain how the approach can be integrated into other core-guided algorithms.

Impact of SAT-Based Preprocessing on Core-Guided MaxSAT Solving

We present a formal analysis of the impact of Boolean satisfiability (SAT) based preprocessing techniques on core-guided solvers for the constraint optimization paradigm of maximum satisfiability (MaxSAT). We analyze the behavior of two solver abstractions of the core-guided approaches. We show that SAT-based preprocessing has no effect on the best-case number of iterations required by the solvers. This implies that, with respect to best-case performance, the potential benefits of applying SAT-based preprocessing in conjunction with core-guided MaxSAT solvers are in principle solely a result of speeding up the individual SAT solver calls made during MaxSAT search. We also show that, in contrast to best-case performance, SAT-based preprocessing can improve the worst-case performance of core-guided approaches to MaxSAT.