On Assigning Prefix Free Codes to the Vertices of a Graph

  • N. S. Narayanaswamy
  • C. E. Veni Madhavan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2108)


For a graph G on n vertices, with positive integer weights w 1,...,w n assigned to the n vertices such that, for every clique K of G, \( \sum\limits_{i \in K} {\frac{1} {{2^{w_i } }}} \leqslant 1 \), the problem we are interested in is to assign binary codes C1,...,C n to the vertices such that C i has w i (or a function of w i) bits in it and, for every edge i, j, C i and C j are not prefixes of each other.We call this the Graph Prefix Free Code Assignment Problem. We relate this new problem to the problem of designing adversaries for comparison based sorting algorithms. We show that the decision version of this problem is as hard as graph colouring and then present results on the existence of these codes for prefect graphs and its subclasses.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • N. S. Narayanaswamy
    • 1
  • C. E. Veni Madhavan
    • 2
  1. 1.Institut für InformatikLudwig Maximilians UniversitätMunichGermany
  2. 2.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

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