On graph powers for leaf-labeled trees

  • Authors:

  • Naomi Nishimura;Prabhakar Ragde;Dimitrios M. Thilikos

  • Affiliations:

  • Department of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;Department of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord, Mòdul C5, c/Jordi Girona Salgado, 1-3 E-08034 Barcelona, Spain

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2002

Quantified Score

Hi-index 0.00

Visualization

Abstract

We extend the well-studied concept of a graph power to that of a k-leaf power G of a tree T: G is formed by creating a node for each leaf in the tree and an edge between a pair of nodes if and only if the associated leaves are connected by a path of length at most k. By discovering hidden combinatorial structure of cliques and neighborhoods, we have developed polynomial-time algorithms that, for k = 3 and k = 4, identify whether or not a given graph G is a k-leaf power of a tree T, and if so, produce a tree T for which G is a k-leaf power. We believe that our structural results will form the basis of a solution for more general k. The general problem of inferring hidden tree structure on the basis of leaf relationships shows up in several areas of application.