On the Exact Solution of VSP for General and Structured Graphs: Models and Algorithms

  • Norberto Castillo-García
  • Héctor Joaquín Fraire Huacuja
  • Rodolfo A. Pazos Rangel
  • José A. Martínez Flores
  • Juan Javier González Barbosa
  • Juan Martín Carpio Valadez
Part of the Studies in Computational Intelligence book series (SCI, volume 547)


In this chapter the vertex separation problem (VSP) is approached. VSP is NP-hard with important applications in VLSI, computer language compiler design, and graph drawing, among others. In the literature there are several exact approaches to solve structured graphs and one work that proposes an integer linear programming (ILP) model for general graphs. Nevertheless, the model found in the literature generates a large number of variables and constraints, and the approaches for structured graphs assume that the structure of the graphs is known a priori. In this work we propose a new ILP model based on a precedence representation scheme, an algorithm to identify whether or not a graph has a Grid structure, and a new benchmark of scale-free instances. Experimental results show that our proposed ILP model improves the average computing time of the reference model in 79.38 %, and the algorithm that identifies Grid-structured graphs has an effectiveness of 100 %.



We would like to thank the National Council of Science and Technology of Mexico (CONACYT), the General Direction of Higher Technological Education (DGEST) and the Ciudad Madero Institute of Technology (ITCM) for their financial support. We also thank IBM Academic Initiative for allowing us to use their optimization engine CPLEX v12.5.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Norberto Castillo-García
    • 1
  • Héctor Joaquín Fraire Huacuja
    • 1
  • Rodolfo A. Pazos Rangel
    • 1
  • José A. Martínez Flores
    • 1
  • Juan Javier González Barbosa
    • 1
  • Juan Martín Carpio Valadez
    • 2
  1. 1.Instituto Tecnológico de Ciudad MaderoMaderoMéxico
  2. 2.Instituto Tecnológico de LeónLeónMéxico

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