Triangle-based consistencies for cost function networks

Nguyen, Hiep H.; Bessière, Christian; Givry, Simon de; Schiex, Thomas

doi:10.1007/s10601-016-9250-1

Cited by 8 publications

(15 citation statements)

References 17 publications

(30 reference statements)

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“…Ties are broken by a lexicographic ordering on the scope of the cliques. We keep also all cliques found of arity 3 because they are natively managed by the ToulBar2 solver as ternary/triangle cost functions with dedicated EDAC soft arc consistency [35,31].…”

Section: Clique Selection and Ordering Heuristicmentioning

confidence: 99%

“…In this case, triangle-based consistencies[31] achieve the same effect, but not in arbitrary arity cliques.…”

mentioning

confidence: 94%

“…In weighted constraint satisfaction, adding cuts remains under explored so far. Instead, research has focused on other local techniques such as on-the-fly variable elimination [24], soft arc consistency [25,16,8,9,28,27,31], dominance detection [26,14], or global techniques like mini-bucket elimination [21] and treedecomposition based search [20,29,15,12,1].…”

Section: Introductionmentioning

confidence: 99%

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Clique Cuts in Weighted Constraint Satisfaction

Givry¹,

Katsirelos²

2017

Lecture Notes in Computer Science

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In integer programming, cut generation is crucial for improving the tightness of the linear relaxation of the problem. This is relevant for weighted constraint satisfaction problems (WCSPs) in which we use approximate dual feasible solutions to produce lower bounds during search. Here, we investigate using one class of cuts in WCSP: clique cuts. We show that clique cuts are likely to trigger suboptimal behavior in the specialized algorithms that are used in WCSP for generating dual bounds and show how these problems can be corrected. At the same time, the additional structure present in WCSP allows us to slightly generalize these cuts. Finally, we show that cliques exist in instances from several benchmark families and that exploiting them can lead to substantial performance improvement.

show abstract

Section: Clique Selection and Ordering Heuristicmentioning

confidence: 99%

“…In this case, triangle-based consistencies[31] achieve the same effect, but not in arbitrary arity cliques.…”

mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Clique Cuts in Weighted Constraint Satisfaction

Givry¹,

Katsirelos²

2017

Lecture Notes in Computer Science

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“…The dual of this LP relaxation minimizes an upper bound on the WCSP optimal value over reparametrizations (also known as equivalence-preserving transformations) of the original WCSP instance. For large instances, this is done only approximately, by methods based on block-coordinate descent [7,8,9,10,2,11] or constraint propagation [12,13,2,14]. Fixed points of these methods are characterized by a local consistency of the CSP formed by the active tuples (to be defined later) of the transformed WCSP [2,7,8,12,9].…”

Section: Introductionmentioning

confidence: 99%

Super-Reparametrizations of Weighted CSPs: Properties and Optimization Perspective

Dlask¹,

Werner²,

Givry³

2022

Preprint

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The notion of reparametrizations of Weighted CSPs (WCSPs) (also known as equivalencepreserving transformations of WCSPs) is well-known and finds its use in many algorithms to approximate or bound the optimal WCSP value. In contrast, the concept of superreparametrizations (which are changes of the weights that keep or increase the WCSP objective for every assignment) was already proposed but never studied in detail. To fill this gap, we present a number of theoretical properties of super-reparametrizations and compare them to those of reparametrizations. Furthermore, we propose a framework for computing upper bounds on the optimal value of the (maximization version of) WCSP using super-reparametrizations. We show that it is in principle possible to employ arbitrary (under some technical conditions) constraint propagation rules to improve the bound. For arc consistency in particular, the method reduces to the known Virtual AC (VAC) algorithm. Newly, we implemented the method for singleton arc consistency (SAC) and compared it to other strong local consistencies in WCSPs on a public benchmark. The results show that the bounds obtained from SAC are superior for many instance groups.

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“…Various local consistencies have been developed for lower bounding in DFBB ( Cooper et al. , 2007 , 2008 ; Givry and Zytnicki, 2005 ; Larrosa and Schiex, 2003 , 2004 ; Nguyen et al. , 2017 ), among which existential directed arc consistency (EDAC) is used the most for its balance between tightness and cost in practice.…”

Section: Introductionmentioning

confidence: 99%

iCFN: an efficient exact algorithm for multistate protein design

Karimi

Shen

2018

Bioinformatics

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MotivationMultistate protein design addresses real-world challenges, such as multi-specificity design and backbone flexibility, by considering both positive and negative protein states with an ensemble of substates for each. It also presents an enormous challenge to exact algorithms that guarantee the optimal solutions and enable a direct test of mechanistic hypotheses behind models. However, efficient exact algorithms are lacking for multistate protein design.ResultsWe have developed an efficient exact algorithm called interconnected cost function networks (iCFN) for multistate protein design. Its generic formulation allows for a wide array of applications such as stability, affinity and specificity designs while addressing concerns such as global flexibility of protein backbones. iCFN treats each substate design as a weighted constraint satisfaction problem (WCSP) modeled through a CFN; and it solves the coupled WCSPs using novel bounds and a depth-first branch-and-bound search over a tree structure of sequences, substates, and conformations. When iCFN is applied to specificity design of a T-cell receptor, a problem of unprecedented size to exact methods, it drastically reduces search space and running time to make the problem tractable. Moreover, iCFN generates experimentally-agreeing receptor designs with improved accuracy compared with state-of-the-art methods, highlights the importance of modeling backbone flexibility in protein design, and reveals molecular mechanisms underlying binding specificity.Availability and implementation https://shen-lab.github.io/software/iCFN Supplementary information Supplementary data are available at Bioinformatics online.

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Triangle-based consistencies for cost function networks

Cited by 8 publications

References 17 publications

Clique Cuts in Weighted Constraint Satisfaction

Clique Cuts in Weighted Constraint Satisfaction

Super-Reparametrizations of Weighted CSPs: Properties and Optimization Perspective

iCFN: an efficient exact algorithm for multistate protein design

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