Exploring the complexity boundary between coloring and list-coloring

Bonomo, Flavia; Durán, Guillermo; Marenco, Javier

doi:10.1007/s10479-008-0391-5

Cited by 33 publications

(40 citation statements)

References 21 publications

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“…The coloring, k-coloring, list-coloring and µ-coloring problem amount to establish if a graph G admits a coloring, a k-coloring, a list coloring and a µ-coloring, respectively. The following complexity results are surveyed in [5]: on interval graphs, the coloring problem and the k-coloring problems are easy, the list coloring and the µ-coloring problems are NP-complete.…”

Section: Problem Descriptionmentioning

confidence: 99%

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An Exact Decomposition Approach for the Real-Time Train Dispatching Problem

Lamorgese

Mannino

2015

Operations Research

110

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Trains’ movements on a railway network are regulated by official timetables. Deviations and delays occur quite often in practice, demanding fast rescheduling and rerouting decisions in order to avoid conflicts and minimize overall delay. This is the real-time train dispatching problem. In contrast with the classic “holistic” approach, we show how to decompose the problem into smaller subproblems associated with the line and the stations. This decomposition is the basis for a master-slave solution algorithm, in which the master problem is associated with the line and the slave problem is associated with the stations. The two subproblems are modeled as mixed integer linear programs, with specific sets of variables and constraints. Similarly to the classical Benders’ decomposition approach, slave and master communicate through suitable feasibility cuts in the variables of the master. Extensive tests on real-life instances from single and double-track lines in Italy showed significant improvements over current dispatching performances. A decision support system based on this exact approach has been in operation in Norway since February 2014 and represents one of the first operative applications of mathematical optimization to train dispatching.

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Section: Problem Descriptionmentioning

confidence: 99%

“…We are nally able to formulate the RTD problem as a Mixed Integer Linear Program by coupling constraints (7) and program (5) and linearizing the objective function:…”

Section: Solution Algorithmmentioning

confidence: 99%

An Exact Decomposition Approach for the Real-Time Train Dispatching Problem

Lamorgese

Mannino

2015

Operations Research

110

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“…However, Fomin et al [24] showed that Coloring is W[1]-hard when parameterized by the clique-width of the input graph. We also note that Precoloring Extension is NP-complete for distance-hereditary graphs [4], which have clique-width at most 3 [29].…”

Section: Parameterized Coloring Problemsmentioning

confidence: 90%

Open Problems on Graph Coloring for Special Graph Classes

Paulusma

2016

Graph-Theoretic Concepts in Computer Science

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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. For a given graph G and integer k, the Coloring problem is that of testing whether G has a k-coloring, that is, whether there exists a vertex mapping c : V → {1, 2, . . .} such that c(u) = c(v) for every edge uv ∈ E. We survey known results on the computational complexity of Coloring for graph classes that are hereditary or for which some graph parameter is bounded. We also consider coloring variants, such as precoloring extensions and list colorings and give some open problems in the area of on-line coloring.

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“…We use, for the reduction, the μ-coloring problem over interval graphs, which was proven to be NP-complete in [9].…”

Section: Np-hardnessmentioning

confidence: 99%

“…Then, we prove that this problem is NP-hard. The key idea is a reduction from the μ-coloring problem over interval graphs, which is known to be NP-hard [9]. Moreover, it is shown that this problem remains NP-hard even when the number of machines is one, and even when the weight function is non-increasing with increasing time.…”

Section: Introductionmentioning

confidence: 99%

Maximizing the Total Weight of Just-In-Time Jobs under Multi-Slot Conditions Is NP-Hard

Chiba

Imahori

2016

IEICE Trans. Inf. & Syst.

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SUMMARYA job is called just-in-time if it is completed exactly on its due date. Under multi-slot conditions, each job has one due date per time slot and has to be completed just-in-time on one of its due dates. Moreover, each job has a certain weight per time slot. We would like to find a just-intime schedule that maximizes the total weight under multi-slot conditions. In this paper, we prove that this problem is NP-hard.

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Exploring the complexity boundary between coloring and list-coloring

Cited by 33 publications

References 21 publications

An Exact Decomposition Approach for the Real-Time Train Dispatching Problem

An Exact Decomposition Approach for the Real-Time Train Dispatching Problem

Open Problems on Graph Coloring for Special Graph Classes

Maximizing the Total Weight of Just-In-Time Jobs under Multi-Slot Conditions Is NP-Hard

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