Reasoning on Interval and Point-based Disjunctive Metric Constraints in Temporal Contexts

Barber, Federico

doi:10.1613/jair.693

Cited by 20 publications

(18 citation statements)

References 34 publications

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“…[3,22,28]. For instance, certain scheduling problems can conveniently be expressed as A-sat(F) with additional constraints on the lengths of the intervals.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…If: Assume h : V → V is a homomorphism from G to H. Then f (as defined below) is a model of I: [3,4],…”

Section: Z Y(s)z; L(z) > L(x) + L(y)} Are Satisfiable If and Only Ifmentioning

confidence: 99%

“…It is easy to check that the resulting set of constraints is satisfiable if and only if G is 3-colorable. For example, if f (x) = [3,4], then constraints of the first type imply that f (v) ∈ { [1,2], [3,4], [5,6]} for any v ∈ V , while the constraints of the second type ensure that the values for "adjacent" variables are distinct.…”

Section: Z Y(s)z; L(z) > L(x) + L(y)} Are Satisfiable If and Only Ifmentioning

confidence: 99%

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Constraint Satisfaction Problems on Intervals and Lengths

Krokhin

Jeavons²,

Jönsson³

2004

SIAM J. Discrete Math.

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. We study interval-valued constraint satisfaction problems (CSPs), in which the aim is to find an assignment of intervals to a given set of variables subject to constraints on the relative positions of intervals. Many well-known problems such as Interval Graph Recognition and Interval Satisfiability can be considered as examples of such CSPs. One interesting question concerning such problems is to determine exactly how the complexity of an interval-valued CSP depends on the set of constraints allowed in instances. For the framework known as Allen's interval algebra this question was completely answered earlier by the authors, by giving a complete description of the tractable cases and showing that all remaining cases are NP-complete.Here we extend the qualitative framework of Allen's algebra with additional constraints on the lengths of intervals. We allow these length constraints to be expressed as Horn disjunctive linear relations, a well-known tractable and sufficiently expressive form of constraints. The class of problems we consider contains, in particular, problems that are very closely related to the previously studied Unit Interval Graph Sandwich problem. We completely characterize sets of qualitative relations for which the CSP augmented with arbitrary length constraints of the above form is tractable. We also show that, again, all the remaining cases are NP-complete.

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“…[3,22,28]. For instance, certain scheduling problems can conveniently be expressed as A-sat(F) with additional constraints on the lengths of the intervals.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…If: Assume h : V → V is a homomorphism from G to H. Then f (as defined below) is a model of I: [3,4],…”

Section: Z Y(s)z; L(z) > L(x) + L(y)} Are Satisfiable If and Only Ifmentioning

confidence: 99%

Section: Z Y(s)z; L(z) > L(x) + L(y)} Are Satisfiable If and Only Ifmentioning

confidence: 99%

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Constraint Satisfaction Problems on Intervals and Lengths

Krokhin

Jeavons²,

Jönsson³

2004

SIAM J. Discrete Math.

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“…A Temporal Constraint Satisfaction Problem (TCSP) is a subtype of CSPs, where variables represent temporal primitives (time points or temporal intervals), such that interpretation domain is the time, variable assignments are temporally ordered and solutions have a temporal interpretation [7], [2]. This is the typical case of scheduling problems, where variables can be instantiated on the time line (see Figure 2) so that they can be associated to starting or ending times of tasks (see Figure 3).…”

Section: Temporal Constraint Satisfaction Problemsmentioning

confidence: 99%

Robustness, stability, recoverability, and reliability in constraint satisfaction problems

Barber

Salido

2014

Knowl Inf Syst

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Abstract. Many real-world problems in Artificial Intelligence (AI) as well as in other areas of computer science and engineering can be efficiently modeled and solved using constraint programming techniques. In many real-world scenarios the problem is partially known, imprecise and dynamic such that some effects of actions are undesired and/or several un-foreseen incidences or changes can occur. Whereas expressivity, efficiency and optimality have been the typical goals in the area, there are several issues regarding robustness that have a clear relevance in dynamic Constraint Satisfaction Problems (CSP). However, there is still no clear and common definition of robustness-related concepts in CSPs. In this paper, we propose two clearly differentiated definitions for robustness and stability in CSP solutions. We also introduce the concepts of recoverability and reliability, which arise in temporal CSPs. All these definitions are based on related well-known concepts, which are addressed in engineering and other related areas.

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“…In general, two techniques are used: Closure and Constraint Satisfaction Problem (CSP) (Barber, 2000).…”

Section: Temporal Constraints Networkmentioning

confidence: 99%

Importance of Flexibility in Manufacturing Systems

Kaschel

Bernal

2006

INT J COMPUT COMMUN

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Flexibility refers to the ability of a manufacturing system to respond cost effectively and rapidly to changing production needs and requirements. This capability is becoming increasingly important for the design and operation of manufacturing systems, as these systems do operate in highly variable and unpredictable environments. It is important to system designers and managers to know of different levels of flexibility and / or determine the amount of flexibility required to achieve a certain level of performance. This paper shows several representations schemes for product flexibility and discusses the usefulness and limitations of each.

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Reasoning on Interval and Point-based Disjunctive Metric Constraints in Temporal Contexts

Cited by 20 publications

References 34 publications

Constraint Satisfaction Problems on Intervals and Lengths

Constraint Satisfaction Problems on Intervals and Lengths

Robustness, stability, recoverability, and reliability in constraint satisfaction problems

Importance of Flexibility in Manufacturing Systems

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