MPLP++: Fast, Parallel Dual Block-Coordinate Ascent for Dense Graphical Models

Tourani, Siddharth; Shekhovtsov, Alexander; Rother, Carsten; Savchynskyy, Bogdan

doi:10.1007/978-3-030-01225-0_16

Cited by 17 publications

(25 citation statements)

References 34 publications

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“…5 The set A * (f ) corresponds to the notion of Bool(f ) in [12]. The characteristic vector of the set A * (f ) was denoted f in [9,2], f in [15], and mi[f ] in [5].…”

Section: Theorem 1 ([2]mentioning

confidence: 99%

“…For assignment x = (a, b) ∈ D V (i.e., x 1 = a, x 2 = b), we have φ(x) = (1, 0, 0, 1, 0, 1, 0, 0) ∈ {0, 1} T where the order of the tuples is given by (9). An example of a WCSP f with this structure is shown in Figure 1a.…”

Section: Theorem 1 ([2]mentioning

confidence: 99%

“…Necessary and sufficient conditions for optimality can be obtained from complementary slackness, see [2,15,5]. Problem (12) has been widely studied [1,2,17,12,4,5,6] and many approaches for its (approximate) large-scale optimization have been proposed, typically based on blockcoordinate descent [8,9,10,2,7,11,20,18] or constraint propagation [12,13,2,27,14]. If f is optimal for (12), then the CSP A * (f ) has a non-empty pairwise-consistency (PWC) closure (for binary WCSPs, PWC reduces to arc consistency) [15].…”

Section: Minimal Upper Bound Over Reparametrizationsmentioning

confidence: 99%

“…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%

“…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%

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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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“…5 The set A * (f ) corresponds to the notion of Bool(f ) in [12]. The characteristic vector of the set A * (f ) was denoted f in [9,2], f in [15], and mi[f ] in [5].…”

Section: Theorem 1 ([2]mentioning

confidence: 99%

Section: Theorem 1 ([2]mentioning

confidence: 99%