Balanced Paths in Colored Graphs

  • Alessandro Bianco
  • Marco Faella
  • Fabio Mogavero
  • Aniello Murano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5734)


We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with the same asymptotic frequency, or (ii) there is a constant which bounds the difference between the occurrences of any two colors for all prefixes of the path. These two notions can be viewed as refinements of the classical notion of fair path, whose simplest form checks whether all colors occur infinitely often. Our notions provide stronger criteria, particularly suitable for scheduling applications based on a coarse-grained model of the jobs involved. We show that both problems are solvable in polynomial time, by reducing them to the feasibility of a linear program.


Colored Graph Balance Problem Difference Vector Difference Path Maximum Modulus 
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 2009

Authors and Affiliations

  • Alessandro Bianco
    • 1
  • Marco Faella
    • 1
  • Fabio Mogavero
    • 1
  • Aniello Murano
    • 1
  1. 1.Università degli Studi di Napoli “Federico II”Italy

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