Generalized edge-rankings of trees

Xiao Zhou, Md Abul Kashem, Takao Nishizeki

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Citations (Scopus)


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 0(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.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 22nd International Workshop, WG 1996, Proceedings
Number of pages15
Publication statusPublished - 1997
Event22nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1996 - Cadenabbia, Italy
Duration: 1996 Jun 121996 Jun 14

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1197 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1996


  • Algorithm
  • Edge-ranking
  • Separator tree
  • Tree


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