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Phase Transition in the Bandwidth Minimization Problem

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MICAI 2009: Advances in Artificial Intelligence (MICAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5845))

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Abstract

It is known that some NP-Complete problems exhibit sharp phase transitions with respect to some order parameter. Moreover, a correlation between that critical behavior and the hardness of finding a solution exists in some of these problems. This paper shows experimental evidence about the existence of a critical behavior in the computational cost of solving the bandwidth minimization problem for graphs (BMPG). The experimental design involved the density of a graph as order parameter, 200000 random connected graphs of size 16 to 25 nodes, and a branch and bound algorithm taken from the literature. The results reveal a bimodal phase transition in the computational cost of solving the BMPG instances. This behavior was confirmed with the results obtained by metaheuristics that solve a known BMPG benchmark.

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Authors and Affiliations

  1. Information Technology Laboratory, CINVESTAV-Tamaulipas, Km. 6 Carretera Victoria-Monterrey, 87276, Victoria Tamps., Mexico

    Nelson Rangel-Valdez & Jose Torres-Jimenez

Authors
  1. Nelson Rangel-Valdez
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  2. Jose Torres-Jimenez
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Editors and Affiliations

  1. Centro de Investigación en Matemáticas, AC. (CIMAT), Area de Computación, Calle Jalisco S/N, Mineral de Valenciana, Guanajuato, CP 36250, Guanajuato, México

    Arturo Hernández Aguirre

  2. Ciencias de la Computación, Tecnológico de Monterrey, Campus Estado de México, Carretera al lago de Guadalupe Km 3,5, Col. Margarita Maza de Juárez, Atizapán de Zaragoza,, CP 52926, Estado de México, México

    Raúl Monroy Borja

  3. Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Ciencias Computacionales, Luis Enrique Erro No. 1, Santa María Tonantzintla, CP 72840, Puebla, México

    Carlos Alberto Reyes Garciá

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© 2009 Springer-Verlag Berlin Heidelberg

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Rangel-Valdez, N., Torres-Jimenez, J. (2009). Phase Transition in the Bandwidth Minimization Problem. In: Aguirre, A.H., Borja, R.M., Garciá, C.A.R. (eds) MICAI 2009: Advances in Artificial Intelligence. MICAI 2009. Lecture Notes in Computer Science(), vol 5845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05258-3_33

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  • DOI: https://doi.org/10.1007/978-3-642-05258-3_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05257-6

  • Online ISBN: 978-3-642-05258-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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