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101
SCIP: solving constraint integer programs
, 2009
"... Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques. In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), wh ..."
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Cited by 122 (0 self)
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Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques. In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), which is free for academic and noncommercial use and can be downloaded in source code. This paper gives an overview of the main design concepts of SCIP and how it can be used to solve constraint integer programs. To illustrate the performance and flexibility of SCIP, we apply it to two different problem classes. First, we consider mixed integer programming and show by computational experiments that SCIP is almost competitive to specialized commercial MIP solvers, even though SCIP supports the more general constraint integer programming paradigm. We develop new ingredients that improve current MIP solving technology. As a second application, we employ SCIP to solve chip design verification problems as they arise in the logic design of integrated circuits. This application goes far beyond traditional MIP solving, as it includes several highly nonlinear constraints, which can be handled nicely within the constraint integer programming framework. We show anecdotally how the different solving techniques from MIP, CP, and SAT work together inside SCIP to deal with such constraint classes. Finally, experimental results show that our approach outperforms current stateoftheart techniques for proving the validity of properties on circuits containing arithmetic.
Bayesian network learning with cutting planes.
 In Proceedings of the TwentySeventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI11),
, 2011
"... Abstract The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer ..."
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Cited by 46 (7 self)
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Abstract The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approachthe search for such cutting planes is effected using a subIP. Results show that this is a particularly fast method for exact BN learning.
NoiseOptimal Capture for High Dynamic Range Photography
"... Taking multiple exposures is a wellestablished approach both for capturing high dynamic range (HDR) scenes and for noise reduction. But what is the optimal set of photos to capture? The typical approach to HDR capture uses a set of photos with geometricallyspaced exposure times, at a fixed ISO set ..."
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Cited by 41 (0 self)
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Taking multiple exposures is a wellestablished approach both for capturing high dynamic range (HDR) scenes and for noise reduction. But what is the optimal set of photos to capture? The typical approach to HDR capture uses a set of photos with geometricallyspaced exposure times, at a fixed ISO setting (typically ISO 100 or 200). By contrast, we show that the capture sequence with optimal worstcase performance, in general, uses much higher and variable ISO settings, and spends longer capturing the dark parts of the scene. Based on a detailed model of noise, we show that optimal capture can be formulated as a mixed integer programming problem. Compared to typical HDR capture, our method lets us achieve higher worstcase SNR in the same capture time (for some cameras, up to 19dB improvement in the darkest regions), or much faster capture for the same minimum acceptable level of SNR. Our experiments demonstrate this advantage for both real and synthetic scenes. 1.
Constraint Integer Programming: a New Approach to integrate CP and MIP
, 2008
"... This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP ..."
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Cited by 34 (7 self)
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This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current stateoftheart commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the nonlinear constraints by employing constraint programming techniques.
Solving MaxCut to optimality by intersecting semidefinite and polyhedral relaxations
, 2008
"... We present a method for finding exact solutions of MaxCut, the problem of finding a cut of maximum weight in a weighted graph. We use a BranchandBound setting, that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a “nearly opti ..."
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Cited by 33 (3 self)
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We present a method for finding exact solutions of MaxCut, the problem of finding a cut of maximum weight in a weighted graph. We use a BranchandBound setting, that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a “nearly optimal” solution of the basic semidefinite MaxCut relaxation, strengthened by triangle inequalities. The expensive part of our bounding procedure is solving the basic semidefinite relaxation of the MaxCut problem, which has to be done several times during the bounding process. We review other solution approaches and compare the numerical results with our method. We also extend our experiments to instances of unconstrained quadratic 01 optimization and to instances of the graph equipartition problem. The experiments show, that our method nearly always outperforms all other approaches. In particular, for dense graphs, where linear programming based methods fail, our method performs very well. Exact solutions are obtained in a reasonable time for any instance of size up to n = 100, independent of the density. For some problems of special structure we can solve even larger problem classes. We could prove optimality for several problems of the literature where, to the best of our knowledge, no other method is able to do so.
Learning to simplify sentences with quasisynchronous grammar and integer programming
 in Proceedings of the Conference on Empirical Methods in Natural Language Processing
"... Text simplification aims to rewrite text into simpler versions, and thus make information accessible to a broader audience. Most previous work simplifies sentences using handcrafted rules aimed at splitting long sentences, or substitutes difficult words using a predefined dictionary. This paper p ..."
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Cited by 24 (1 self)
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Text simplification aims to rewrite text into simpler versions, and thus make information accessible to a broader audience. Most previous work simplifies sentences using handcrafted rules aimed at splitting long sentences, or substitutes difficult words using a predefined dictionary. This paper presents a datadriven model based on quasisynchronous grammar, a formalism that can naturally capture structural mismatches and complex rewrite operations. We describe how such a grammar can be induced from Wikipedia and propose an integer linear programming model for selecting the most appropriate simplification from the space of possible rewrites generated by the grammar. We show experimentally that our method creates simplifications that significantly reduce the reading difficulty of the input, while maintaining grammaticality and preserving its meaning. 1
A Practical Approach to Satisfiability Modulo Linear Integer Arithmetic
 Journal on Satisfiability, Boolean Modeling and Computation
"... We present a detailed description of a theory solver for Linear Integer Arithmetic (LA(Z)) in a lazy SMT context. Rather than focusing on a single technique that guarantees theoretical completeness, the solver makes extensive use of layering and heuristics for combining different techniques in order ..."
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Cited by 18 (3 self)
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We present a detailed description of a theory solver for Linear Integer Arithmetic (LA(Z)) in a lazy SMT context. Rather than focusing on a single technique that guarantees theoretical completeness, the solver makes extensive use of layering and heuristics for combining different techniques in order to achieve good performance in practice. The viability of our approach is demonstrated by an empirical evaluation on a wide range of benchmarks, showing significant performance improvements over current stateoftheart solvers.
Maximum likelihood pedigree reconstruction using integer programming
 in Proceeedings of the Workshop on Constraint Based Methods for Bioinformatics (WCBMB) 2010
"... integer programming ..."
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Feasibility pump 2.0
, 2008
"... Finding a feasible solution of a given MixedInteger Programming (MIP) model is a very important N Pcomplete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a feasible solution to general MIPs that can be viewed as a clever way to round a sequ ..."
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Cited by 13 (1 self)
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Finding a feasible solution of a given MixedInteger Programming (MIP) model is a very important N Pcomplete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a feasible solution to general MIPs that can be viewed as a clever way to round a sequence of fractional solutions of the LP relaxation, until a feasible one is eventually found. In this paper we study the effect of replacing the original rounding function (which is fast and simple, but somehow blind) with more clever rounding heuristics. In particular, we investigate the use of a divinglike procedure based on rounding and constraint propagation— a basic tool in Constraint Programming. Extensive computational results on binary and general integer MIPs from the literature show that the new approach produces a substantial improvement of the FP success rate, without slowingdown the method and with a significantly better quality of the feasible solutions found.
Automatic generation of story highlights
 In Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics
, 2010
"... In this paper we present a joint content selection and compression model for singledocument summarization. The model operates over a phrasebased representation of the source document which we obtain by merging information from PCFG parse trees and dependency graphs. Using an integer linear program ..."
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Cited by 13 (2 self)
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In this paper we present a joint content selection and compression model for singledocument summarization. The model operates over a phrasebased representation of the source document which we obtain by merging information from PCFG parse trees and dependency graphs. Using an integer linear programming formulation, the model learns to select and combine phrases subject to length, coverage and grammar constraints. We evaluate the approach on the task of generating “story highlights”—a small number of brief, selfcontained sentences that allow readers to quickly gather information on news stories. Experimental results show that the model’s output is comparable to humanwritten highlights in terms of both grammaticality and content. 1