Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this article, we study the (k,c)-coloring problem, a generalization of the vertex coloring problem where we have to assign k colors to each vertex of an undirected graph, and two adjacent vertices can share at most c colors. We propose a new formulation for the (k,c)-coloring problem and develop a Branch-and-Price algorithm. We tested the algorithm on instances having from 20 to 80 vertices and different combinations for k and c, and compare it with a recent algorithm proposed in the literature. Computational results show that the overall approach is effective and has very good performance on instances where the previous algorithm fails. © 2014 Wiley Periodicals, Inc. NETWORKS, 2014 Vol. 65(4), 353-366 2015 © 2014 Wiley Periodicals, Inc.

Registro:

Documento: Artículo
Título:A branch-and-price algorithm for the (k,c)-coloring problem
Autor:Malaguti, E.; Méndez-Díaz, I.; José Miranda-Bront, J.; Zabala, P.
Filiación:DEI, University of Bologna, Viale Risorgimento 2, Bologna, 40136, Italy
Department of Computer Science, FCEyN, University of Buenos Aires, Buenos Aires, Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Palabras clave:branch-and-price; column generation; computational experiments; frequency assignment; heuristics; multicoloring; vertex coloring; Coloring; Costs; Integer programming; Linear programming; Branch and price; Column generation; Computational experiment; Frequency assignments; heuristics; Multicoloring; Vertex coloring; Algorithms
Año:2015
Volumen:65
Número:4
Página de inicio:353
Página de fin:366
DOI: http://dx.doi.org/10.1002/net.21579
Título revista:Networks
Título revista abreviado:Networks
ISSN:00283045
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00283045_v65_n4_p353_Malaguti

Referencias:

  • Aardal, K., Van Hoesel, S., Koster, A., Mannino, C., Sassano, A., Models and solution techniques for the frequency assignment problem (2003) 4OR, 1, pp. 261-317
  • Farley, A.A., A note on bounding a class of linear programming problems, including cutting stock problems (1990) Oper Res, 38, pp. 922-923
  • Furini, F., Malaguti, E., Exact weighted vertex coloring via branch-and-price (2012) Discrete Optim, 9, pp. 130-136
  • Garey, M., Johnson, D., Computers and intractability: A guide to the theory of NP-completeness (1979) DIMACS Series in Discrete Mathematics and Theoretical Computer Science, , Freeman, New York
  • Gualandi, S., Malucelli, F., Exact solution of graph coloring problems via constraint programming and column generation (2012) INFORMS J Comput, 24, pp. 81-100
  • Halldõrsson, M., Kortsarz, G., Multicoloring: Problems and techniques, mathematical foundations of computer science 2004 (2004) Lect Notes Comput Sci, 3153, pp. 25-41
  • Held, S., Cook, W., Sewell, E., Maximum-weight stable sets and safe lower bounds for graph coloring (2012) Math Program Comput, 4, pp. 363-381
  • Hoshino, E., Frota, Y., De Souza, C.C., A branch-and-price approach for the partition coloring problem (2011) Oper Res Lett, 39, pp. 132-137
  • Konc, J., Janezic, D., An improved branch and bound algorithm for the maximum clique problem (2007) MATCH Commun Math Comput Chem, 58, pp. 569-590
  • Koster, A., Tieves, M., Column generation for frequency assignment in slow frequency hopping networks (2012) EURASIP J Wireless Commun Networking, 253, pp. 1-14
  • Koster, A., Zymolka, A., Tight LP-based lower bounds for wavelength conversion in optical networks (2007) Stat Neerl, 61, pp. 115-136
  • Malaguti, E., The vertex coloring problem and its generalizations (2009) 4OR Q J Oper Res, 7, pp. 101-104
  • Malaguti, E., Méndez-Díaz, I., Miranda-Bront, J., Zabala, P., Coloring via column generation (2013) Electron Notes Discrete Math, 41, pp. 447-454
  • Malaguti, E., Monaci, M., Toth, P., An exact approach for the vertex coloring problem (2011) Discrete Optim, 8, pp. 174-190
  • Malaguti, E., Toth, P., A survey on vertex coloring problems (2010) Int Trans Oper Res, 17, pp. 1-34
  • Mehrotra, A., Trick, M., A column generation approach for graph coloring (1996) INFORMS J Comput, 8, pp. 344-354
  • Mehrotra, A., Trick, M., A branch-and-price approach for graph multicoloring (2007) Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies, Operations Research/Computer Science Interfaces Series, 37, pp. 15-29. , E. Baker, A. Joseph, A. Mehrotra, and M. Trick (Editors), Springer
  • Méndez-Díaz, I., Zabala, P., A branch-and-cut algorithm for graph coloring (2006) Discrete Appl Math, 154, pp. 826-847
  • Méndez-Díaz, I., Zabala, P., A cuttting plane algorithm for graph coloring (2008) Discrete Appl Math, 156, pp. 159-179
  • Méndez-Díaz, I., Zabala, P., The (k, k - 1) coloring problem (2008) Proc Int Symp Comb Optim, , Warwick, UK
  • Méndez-Díaz, I., Zabala, P., Solving a multicoloring problem with overlaps using integer programming (2010) Discrete Appl Math, 158, pp. 349-354
  • Zymolka, A., (2006) Design of Survivable Optical Networks by Mathematical Optimization, Ph.D. Thesis, , TU Berlin

Citas:

---------- APA ----------
Malaguti, E., Méndez-Díaz, I., José Miranda-Bront, J. & Zabala, P. (2015) . A branch-and-price algorithm for the (k,c)-coloring problem. Networks, 65(4), 353-366.
http://dx.doi.org/10.1002/net.21579
---------- CHICAGO ----------
Malaguti, E., Méndez-Díaz, I., José Miranda-Bront, J., Zabala, P. "A branch-and-price algorithm for the (k,c)-coloring problem" . Networks 65, no. 4 (2015) : 353-366.
http://dx.doi.org/10.1002/net.21579
---------- MLA ----------
Malaguti, E., Méndez-Díaz, I., José Miranda-Bront, J., Zabala, P. "A branch-and-price algorithm for the (k,c)-coloring problem" . Networks, vol. 65, no. 4, 2015, pp. 353-366.
http://dx.doi.org/10.1002/net.21579
---------- VANCOUVER ----------
Malaguti, E., Méndez-Díaz, I., José Miranda-Bront, J., Zabala, P. A branch-and-price algorithm for the (k,c)-coloring problem. Networks. 2015;65(4):353-366.
http://dx.doi.org/10.1002/net.21579