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Linear Layout Problems

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Handbook of Heuristics

Abstract

The term layout problem comes from the context of Very Large-Scale Integration (VLSI) circuit design. Graph layouts are optimization problems where the main objective is to project an original graph into a predefined host graph, usually a horizontal line. In this paper, some of the most relevant linear layout problems are reviewed, where the purpose is to minimize the objective function: the Cutwidth, the Minimum Linear Arrangement, the Vertex Separation, the SumCut, and the Bandwidth. Each problem is presented with its formal definition and it is illustrated with a detailed example. Additionally, the most relevant heuristic methods in the associated literature are reviewed together with the instances used in their evaluation. Since linear layouts represent a challenge for optimization methods in general and, for heuristics in particular, this review pays special attention to the strategies and methodologies which provide high-quality solutions.

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Acknowledgements

This research has been partially supported by Fondo Europeo de Desarrollo Regional (FEDER) and Ministerio de Economía y Competitividad (MINECO) of Spain. Grant Ref. TIN2015-65460-C2 (MINECO/FEDER).

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Authors and Affiliations

  1. Dept. of Sistemas Informáticos, Universidad Politécnica de Madrid, Ctra. de Valencia, Km. 7, 28031, Madrid, Spain

    Eduardo G. Pardo

  2. Dept. of Statistics and Operations Research, Universidad de Valencia, Burjassot (Valencia), Spain

    Rafael Martí

  3. Dept. of Ciencias de la Computación, Universidad Rey Juan Carlos, Móstoles, Móstoles (Madrid), Spain

    Abraham Duarte

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  1. Eduardo G. Pardo
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  2. Rafael Martí
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  3. Abraham Duarte
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Correspondence to Eduardo G. Pardo .

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  1. Department of Statistics and Operations, University of Valencia, Valencia, Spain

    Rafael Martí

  2. University of Florida Industrial and Systems Engineering, Gainesville, Florida, USA

    Pardalos Panos

  3. AT & T Labs Research, Florham Park, New Jersey, USA

    Mauricio G.C. Resende

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Pardo, E.G., Martí, R., Duarte, A. (2016). Linear Layout Problems. In: Martí, R., Panos, P., Resende, M. (eds) Handbook of Heuristics. Springer, Cham. https://doi.org/10.1007/978-3-319-07153-4_45-1

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