Algorithms for generalized vertex-rankings of partial k-trees

Md Abul Kashem, Xiao Zhou, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


A c-vertex-ranking of a graph G for a positive integer c is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i. A c-vertex-ranking is optimal if the number of labels used is as small as possible. We present sequential and parallel algorithms to find an optimal c-vertex-ranking of a partial k-tree, that is, a graph of treewidth bounded by a fixed integer k. The sequential algorithm takes polynomial-time for any positive integer c. The parallel algorithm takes O(log n) parallel time using a polynomial number of processors on the common CRCW PRAM, where n is the number of vertices in G.

Original languageEnglish
Pages (from-to)407-427
Number of pages21
JournalTheoretical Computer Science
Issue number2
Publication statusPublished - 2000 Jun 17


  • Algorithm
  • Partial k-tree
  • Separator tree
  • Treewidth
  • Vertex-ranking


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