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Exact Algorithms for Coloring Graphs While Avoiding Monochromatic Cycles

  • Fabrice Talla Nobibon
  • Cor Hurkens
  • Roel Leus
  • Frits C. R. Spieksma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)

Abstract

We consider the problem of deciding whether a given directed graph can be vertex partitioned into two acyclic subgraphs. Applications of this problem include testing rationality of collective consumption behavior, a subject in micro-economics. We identify classes of directed graphs for which the problem is easy and prove that the existence of a constant factor approximation algorithm is unlikely for an optimization version which maximizes the number of vertices that can be colored using two colors while avoiding monochromatic cycles. We present three exact algorithms, namely an integer-programming algorithm based on cycle identification, a backtracking algorithm, and a branch-and-check algorithm. We compare these three algorithms both on real-life instances and on randomly generated graphs. We find that for the latter set of graphs, every algorithm solves instances of considerable size within few seconds; however, the CPU time of the integer-programming algorithm increases with the number of vertices in the graph while that of the two other procedures does not. For every algorithm, we also study empirically the transition from a high to a low probability of YES answer as function of a parameter of the problem. For real-life instances, the integer-programming algorithm fails to solve the largest instance after one hour while the other two algorithms solve it in about ten minutes.

Keywords

Directed Graph Exact Algorithm Color Class Strongly Connect Component Dominance Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Fabrice Talla Nobibon
    • 1
  • Cor Hurkens
    • 2
  • Roel Leus
    • 1
  • Frits C. R. Spieksma
    • 1
  1. 1.Operations Research GroupUniversity of LeuvenLeuvenBelgium
  2. 2.Department of Mathematics and Computer Science.Eindhoven University of TechnologyEindhoventhe Netherlands

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