Sequencing and Counting with the multicost-regular Constraint

Menana, Julien; Demassey, Sophie

doi:10.1007/978-3-642-01929-6_14

Cited by 26 publications

(14 citation statements)

References 10 publications

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“…We note that Lagrangian relaxations have been applied before in the context of CP, see for example [16,17,18,19,20,21,22,23]. Our results further strengthen the idea that Lagrangian relaxations are a particularly useful method from operations research for enhancing the inference process of constraint programming.…”

Section: Introductionsupporting

confidence: 75%

A Lagrangian Relaxation for Golomb Rulers

Slusky

Hoeve

2013

Lecture Notes in Computer Science

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Abstract. The Golomb Ruler Problem asks to position n integer marks on a ruler such that all pairwise distances between the marks are distinct and the ruler has minimum total length. It is a very challenging combinatorial problem, and provably optimal rulers are only known for n up to 26. Lower bounds can be obtained using Linear Programming formulations, but these are computationally expensive for large n. In this paper, we propose a new method for finding lower bounds based on a Lagrangian relaxation. We present a combinatorial algorithm that finds good bounds quickly without the use of a Linear Programming solver. This allows us to embed our algorithm into a constraint programming search procedure. We compare our relaxation with other lower bounds from the literature, both formally and experimentally. We also show that our relaxation can reduce the constraint programming search tree considerably.

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Section: Introductionsupporting

confidence: 75%

A Lagrangian Relaxation for Golomb Rulers

Slusky

Hoeve

2013

Lecture Notes in Computer Science

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“…The latter condition can entail a wide variety of constraints. Previous works [11] [13] used allowed (or forbidden) patterns to express successive shift constraints. For example, with 3 shifts of 8 hours per day: D (day), E (evening) and N (night), ND can be forbidden since employees need some rest after night shifts.…”

Section: Crew-rosteringmentioning

confidence: 99%

An Optimal Arc Consistency Algorithm for a Chain of Atmost Constraints with Cardinality

Siala

Hébrard

Huguet

2012

Lecture Notes in Computer Science

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Abstract. The ATMOSTSEQCARD constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n − q + 1 constraints ATMOST u on each subsequence of size q. This constraint is useful in car-sequencing and crew-rostering problems. In [18], two algorithms designed for the AMONGSEQ constraint were adapted to this constraint with a O(2 q n) and O(n 3 ) worst case time complexity, respectively. In [10], another algorithm with a O(n 2 log n) worst case time complexity and similarly adaptable to filter ATMOSTSEQCARD in O(n log n) was proposed. In this paper, we introduce an algorithm for achieving Arc Consistency on the ATMOSTSEQCARD constraint with a O(n) (hence optimal) worst case time complexity. We then empirically study the efficiency of our propagator on instances of the car-sequencing and crew-rostering problems.

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“…The cost-regular constraint [12] as well as multi-cost [20] extend regular by maintaining a cost variable. However, these costs are set on the variable/value pairs, whereas we need to represent the probabilities of a continuation given all contexts.…”

Section: Propagators For Elementary Markov Constraintsmentioning

confidence: 99%

Markov constraints: steerable generation of Markov sequences

Pachet¹,

Roy²

2010

Constraints

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Markov chains are a well known tool to model temporal properties of many phenomena, from text structure to fluctuations in economics. Because they are easy to generate, Markovian sequences, i.e. temporal sequences having the Markov property, are also used for content generation applications such as text or music generation that imitate a given style. However, Markov sequences are traditionally generated using greedy, left-to-right algorithms. While this approach is computationally cheap, it is fundamentally unsuited for interactive control. This paper addresses the issue of generating steerable Markovian sequences. We target interactive applications such as games, in which users want to control, through simple input devices, the way the system generates a Markovian sequence, such as a text, a musical sequence or a drawing. To this aim, we propose to revisit Markov sequence generation as a branch and bound constraint satisfaction problem (CSP). We propose a CSP formulation of the basic Markovian hypothesis as elementary Markov Constraints (EMC). We propose algorithms that achieve domain-consistency for the propagators of EMCs, in an event-based implementation of CSP. We show how EMCs can be combined to estimate the global Markovian probability of a whole sequence, and accommodate for different species of Markov generation such as fixed order, variable-order, or smoothing. Such a formulation, although more costly than traditional greedy generation algorithms, yields the immense advantage of being naturally steerable, since control specifications can be represented by arbitrary additional constraints, without any modification of the generation algorithm. We illustrate our approach on simple yet combinatorial chord sequence and melody generation problems and give some performance results.

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Sequencing and Counting with the multicost-regular Constraint

Cited by 26 publications

References 10 publications

A Lagrangian Relaxation for Golomb Rulers

A Lagrangian Relaxation for Golomb Rulers

An Optimal Arc Consistency Algorithm for a Chain of Atmost Constraints with Cardinality

Markov constraints: steerable generation of Markov sequences

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