Generalized edge-rankings of trees

Extended abstract
  • Xiao Zhou
  • Md. Abul Kashem
  • Takao Nishizeki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1197)


In this paper we newly define a generalized edge-ranking of a graph G as follows: for a positive integer c, a c-edge-ranking of G is a labeling (ranking) of the edges of G with integers such that, for any label i, deletion of all edges with labels > i leaves connected components, each having at most c edges with label i. The problem of finding an optimal c-edge-ranking of G, that is, a c-edge-ranking using the minimum number of ranks, has applications in scheduling the manufacture of complex multi-part products; it is equivalent to finding a c-edge-separator tree of G having the minimum height. We present an algorithm to find an optimal c-edge-ranking of a given tree T for any positive integer c in time O(n2 log δ), where n is the number of vertices in T and δ is the maximum vertex-degree of T. Our algorithm is faster than the best algorithm known for the case c=1.

Key words

Algorithm Edge-ranking Separator tree Tree 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Xiao Zhou
    • 1
  • Md. Abul Kashem
    • 2
  • Takao Nishizeki
    • 2
  1. 1.Education Center for Information ProcessingTohoku UniversitySendaiJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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