Exact Algorithms for L(2,1)-Labeling of Graphs

  • Jan Kratochvíl
  • Dieter Kratsch
  • Mathieu Liedloff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)


The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph G = (V,E) into an interval of integers [0..k] is an L(2,1)-labeling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed k ≥ 4, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive O((k + 1) n ) algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of k = 4 – here the running time of our algorithm is O(1.3161 n ).


Dynamic Programming Exact Algorithm Adjacent Vertex Common Neighbor Label Vertex 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jan Kratochvíl
    • 1
  • Dieter Kratsch
    • 2
  • Mathieu Liedloff
    • 2
  1. 1.Department of Applied Mathematics, and Institute for Theoretical Computer Science, Charles University, Malostranské nám. 25, 118 00 Praha 1Czech Republic
  2. 2.Laboratoire d’Informatique Théorique et Appliquée, Université Paul Verlaine - Metz, 57045 Metz Cedex 01France

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