MDD propagators with explanation

Gange, Graeme; Stuckey, Peter J.; Szymanek, Radosław

doi:10.1007/s10601-011-9111-x

Cited by 24 publications

(16 citation statements)

References 18 publications

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“…The mddc algorithm was made incremental in [3] to deal with this issue. Here, we show that STR2's value-accumulation phase can be made incremental as well, although this does not make STR2w optimal in the worst case (see [6,9] for optimal algorithms).…”

Section: Discussionmentioning

confidence: 99%

Improving the lower bound of simple tabular reduction

2014

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Simple Tabular Reduction (STR) is a state-of-the-art filtering technique for enforcing Generalized Arc Consistency (GAC) on positive table constraints. Despite its good performance in practice, the STR2 algorithm suffers from a mandatory lower bound equal to the number of domain values in the current state of the problem, because the presence of each value must be justified every time STR2 is called. We overcome this fixed cost by redesigning STR2 and incorporating watched tuples. Experiments show that the revised algorithm is better at coping with problems that involve a large number of small changes during search and it can be more than twice as fast on certain structured problems.

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Section: Discussionmentioning

confidence: 99%

Improving the lower bound of simple tabular reduction

2014

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“…A number of MDD based algorithms have been proposed, including Mddc,incremental-MDD (Gange, Stuckey, and Szymanek 2011), MDD4 (Perez and Régin 2014), Compact-MDD (Compact-Diagram) (Verhaeghe, Lecoutre, and Schaus 2018;, and BDDF (Vion and Piechowiak 2018). The Mddc is the first MDD based filtering algorithm.…”

Section: Multi-valued Decision Diagrammentioning

confidence: 99%

“…Incrementality techniques appear in many (G)AC algorithms: (i) In the AC4 algorithm, the number of valid supports of variable values are recorded during search, correspondingly a variable value is not AC if the number of valid supports on a constraint is zero; (ii) In the AC6, AC7, GACscheme based, (G)AC2001/3.1/3.2/3.3, STR3, STRbit and STRbit-C algorithms, the last valid support of each variable value is maintained, thus, we only need to consider the supports before the last support when the last support becomes invalid; (iii) In the STR based algorithms, current tables, i.e., invalid tuples are removed, are maintained by using sparse (bit-)sets; (iv) In the GAC4 algorithm (Mohr and Masini 1988), the valid supports of each variable value are maintained by using linked lists or sparse sets; (v) In the Mddc, MDD4(R), incremental-MDD (Gange, Stuckey, and Szymanek 2011) and BDDF (Vion and Piechowiak 2018) algorithms, valid nodes are maintained by using various data structures, in addition, valid edges are also maintained in MDD4(R) and incremental-MDD. Note that a valid tuple corresponds to a path consisting of valid nodes and edges.…”

Section: Incrementalitymentioning

confidence: 99%

Generalized Arc Consistency Algorithms for Table Constraints: A Summary of Algorithmic Ideas

Yap

Xia

Wang

2020

AAAI

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Constraint Programming is a powerful paradigm to model and solve combinatorial problems. While there are many kinds of constraints, the table constraint (also called a CSP) is perhaps the most significant—being the most well-studied and has the ability to encode any other constraints defined on finite variables. Thus, designing efficient filtering algorithms on table constraints has attracted significant research efforts. In turn, there have been great improvements in efficiency over time with the evolution and development of AC and GAC algorithms. In this paper, we survey the existing filtering algorithms for table constraint focusing on historically important ideas and recent successful techniques shown to be effective.

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“…It is a multiple-valued extension of BDDs [6]. An MDD, as used in CP [1,13,14,3,11], is a rooted directed acyclic graph (DAG) used to represent some multivalued function f : {0...d − 1} r → {true, false}, based on a given integer d. Given the r input variables, the DAG representation is designed to contain r layers of nodes, such that each variable is represented at a specific layer of the graph. Each node on a given layer has at most d outgoing arcs to nodes in the next layer of the graph (i.e.…”

Section: Introductionmentioning

confidence: 99%

Constructions and In-Place Operations for MDDs Based Constraints

Perez¹,

Régin²

2016

Lecture Notes in Computer Science

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International audienceThis papers extends in three ways our previous work about efficient operations on Multi-valued Decision Diagrams (MDD) for building Constraint Programming models. First, we improve the existing methods for transforming a set of tuples, Global Cut Seeds or sequences of tuples into MDDs. Then, we present in-place algorithms for adding and deleting tuples from an MDD. Finally, we describe an incremental version of an algorithm which reduces an MDD. We show on a real-life application that in-place operations on MDDs combined with this incremental algorithm outperform classical operations. Furthermore, we give some experimental results showing that the creation algorithms we propose strongly improve upon existing ones

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MDD propagators with explanation

Cited by 24 publications

References 18 publications

Improving the lower bound of simple tabular reduction

Improving the lower bound of simple tabular reduction

Generalized Arc Consistency Algorithms for Table Constraints: A Summary of Algorithmic Ideas

Constructions and In-Place Operations for MDDs Based Constraints

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