Comparative Study on Constructive Heuristics for the Vertex Separation Problem

  • Norberto Castillo-García
  • Héctor Joaquín Fraire HuacujaEmail author
  • José Antonio Martínez Flores
  • Rodolfo A. Pazos Rangel
  • Juan Javier González Barbosa
  • Juan Martín Carpio Valadez
Part of the Studies in Computational Intelligence book series (SCI, volume 601)


The vertex separation problem (VSP) consists of finding a linear ordering of the vertices of an input graph that minimizes the maximum number of vertex separators at each cut-point induced by the ordering. VSP is an NP-hard problem whose efficient solution is relevant in fields such as very large scale integration design, computer language compiler design, graph drawing and bioinformatics. In the literature reviewed, we found several exact algorithms and two metaheuristics based on the variable neighborhood search approach. These metaheuristics are currently the best stochastic algorithms for solving VSP. One of the key points of their efficiency is the usage of heuristics to construct a high-quality initial solution that considerably improves the algorithm performance. In this chapter we augment the literature on VSP by proposing a new set of heuristics. The proposed constructive heuristics are compared with the best ones found in the state-of-the-art and with random solution generator (Rnd). Experimental results demonstrate the importance of constructive algorithms. The best constructive improves Rnd by 89.96 % in solution quality.


  1. 1.
    Duarte, A., Escudero, L., Martí, R., Mladenovic, N., Pantrigo, J., Sánchez-Oro, J.: Variable neighborhood search for the vertex separation problem. Comput. Oper. Res. 39(12), 3247–3255 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Suv. 34(3), 313–356 (2002)CrossRefGoogle Scholar
  3. 3.
    Lengauer, T.: Black-white pebbles and graph separation. Acta Informatica 16, 465–475 (1981)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Díaz, J., Penrose, M.D., Petit, J., Serna, M.: Approximating layout problems on random geometric graphs. J. Algorithms 39(1), 78–116 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Goldberg, P.W., Golumbic, M.C., Kaplan, H., Shamir, R.: Four strikes against physical mapping of DNA. J. Comput. Biol. 2(1), 139–152 (1995)CrossRefGoogle Scholar
  6. 6.
    Gusted, J.: On the path width of chordal graphs. Discrete Appl. Math. 45(3), 233–248 (1993)Google Scholar
  7. 7.
    Monien, B., Sudborough, I.H.: Min cut is np-complete for edge weighted trees. Theor. Comput. Sci. 58(1–3), 209–229 (1988)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Leiserson, C.: Area-efficient graph layouts (for VLSI). In: Proceedings of IEEE Symposium on Foundations of Computer Science, pp. 270–281 (1980)Google Scholar
  9. 9.
    Bodlaender, H., Gustedt, J., Telle, J.: Linear time register allocation for a fixed number of registers. In: Proceedings of the Symposium on Discrete Algorithms (1998)Google Scholar
  10. 10.
    Kornai, A.: Narrowness, path-width, and their application in natural language processing. Discrete Appl. Math. 36, 87–92 (1997). (Elsevier Science Publishers B. V. (1992))Google Scholar
  11. 11.
    Lopes, I., de Carvalho, J.: Minimization of open orders using interval graphs. IAENG Int. J. Appl. Math. 40(4), 297–306 (2010)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Luque, G., Alba, E.: Metaheuristics for the DNA fragment assembly problem. Int. J. Comput. Intell. Res. 1(2), 98–108 (2005)CrossRefGoogle Scholar
  13. 13.
    Sánchez-Oro, J., Pantrigo, J., Duarte, A.: Combining intensification and diversification strategies in VNS. An application to the Vertex separation problem. Comput. Oper. Res. 52(part B), 209–219 (2013)Google Scholar
  14. 14.
    VSPLIB 2012. Home page:
  15. 15.
    Pantrigo, J.J., Martí, R., Duarte, A., Pardo, E.G.: Scatter search for the cutwidth minimization problem. Ann. Oper. Res. 199(1), 285–304 (2012)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Norberto Castillo-García
    • 1
  • Héctor Joaquín Fraire Huacuja
    • 1
    Email author
  • José Antonio Martínez Flores
    • 1
  • Rodolfo A. Pazos Rangel
    • 1
  • Juan Javier González Barbosa
    • 1
  • Juan Martín Carpio Valadez
    • 2
  1. 1.Tecnológico Nacional de MéxicoInstituto Tecnológico de Ciudad MaderoCiudad MaderoMexico
  2. 2.Tecnológico Nacional de MéxicoInstituto Tecnológico de LeónLeónMexico

Personalised recommendations