Efficient algorithms for interval graphs and circular‐arc graphs

Gupta, Udaiprakash I.; Lee, D. T.; Leung, Joseph Y.-T.

doi:10.1002/net.3230120410

Cited by 223 publications

(114 citation statements)

References 8 publications

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“…Indeed, thanks to Lemma 3.1, we know that in this case the graph G(y s ) is interval. Then nding an inequality of type (8.iii) violated by y amounts to nding, for each s, a maximum cardinality clique in the interval graph G(y s ), which can be done in |T | log |T | (see [19]). …”

Section: Solution Algorithmmentioning

confidence: 99%

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

Lamorgese

Mannino

2015

Operations Research

113

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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: Solution Algorithmmentioning

confidence: 99%

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

Lamorgese

Mannino

2015

Operations Research

113

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“…The next lemma is central in the proof of the logarithmic upper bound. This lemma requires the following classical linear-time and space algorithm for partitioning interval graphs into cliques (see for example [15]). …”

Section: Proofmentioning

confidence: 99%

“…These cliques form a partition of the interval graph G into cliques. By picking the interval having the smallest right endpoint in each clique C j , we obtain a maximum stable of G, which implies that this partition is minimum [15]. Thus, such a partition into cliques shall be called canonical throughout the paper.…”

Section: Proofmentioning

confidence: 99%

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On partitioning interval graphs into proper interval subgraphs and related problems

Gardi¹

2010

J. Graph Theory

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In this paper, we establish that any interval graph (resp. circular-arc graph) with n vertices admits a partition into at most ⌈log 3 n⌉ (resp. ⌈log 3 n⌉ + 1) proper interval subgraphs, for n > 1. The proof is constructive and provides an efficient algorithm to compute such a partition. On the other hand, this bound is shown to be asymptotically sharp for an infinite family of interval graphs. In addition, some results are derived for related problems.

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“…The power fading value p i covering the maximum number of testpoints in Z can therefore be computed by finding a clique of maximum size in an interval graph G. This can be done in O Z log Z (Gupta et al 1982). …”

Section: A Grasp Algorithm For Nplanmentioning

confidence: 99%

The Network Packing Problem in Terrestrial Broadcasting

Mannino

Rossi

Smriglio

2006

Operations Research

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The introduction of digital terrestrial broadcasting all over Europe requires a complete and challenging replanning of in-place analog systems. However, an abrupt migration of resources (transmitters and frequencies) from analog to digital networks cannot be accomplished because the analog services must be preserved temporarily. Hence, a multiobjective problem arises, in which several networks sharing a common set of resources have to be designed. This problem is referred to as the network packing problem. In Italy, this problem is particularly challenging because of a large number of transmitters, orographical features, and strict requirements imposed by Italian law. In this paper, we report our experience in developing solution methods at the major Italian broadcaster Radiotelevisione Italiana (RAI S.p.A.). We propose a two-stage heuristic. In the first stage, emission powers are assigned to each network separately. In the second stage, frequencies are assigned to all networks so as to minimize the loss from mutual interference. A software tool incorporating our methodology is currently in use at RAI to help discover and select high-quality alternatives for the deployment of digital equipment.Subject classifications: communications: frequency and power assignment; integer programming, heuristic: neighborhood search. Area of review: OR Practice.

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Efficient algorithms for interval graphs and circular‐arc graphs

Cited by 223 publications

References 8 publications

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

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

On partitioning interval graphs into proper interval subgraphs and related problems

The Network Packing Problem in Terrestrial Broadcasting

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