A polynomial algorithm to compute the minimum degree spanning trees of directed acyclic graphs with applications to the broadcast problem

  • Yao G
  • Zhu D
  • Li H
 et al. 
  • 12

    Readers

    Mendeley users who have this article in their library.
  • 6

    Citations

    Citations of this article.

Abstract

In this paper, we focus on the directed minimum degree spanning tree problem and the minimum time broadcast problem. Firstly, we propose a polynomial time algorithm for the minimum degree spanning tree problem in directed acyclic graphs. The algorithm starts with an arbitrary spanning tree, and iteratively reduces the number of vertices of maximum degree. We can prove that the algorithm must reduce a vertex of the maximum degree for each phase, and finally result in an optimal tree. The algorithm terminates in O (mn log n) time, where m and n are the numbers of edges and vertices of the graph, respectively. Moreover, we apply the new algorithm to the minimum time broadcast problem. Two consequences for directed acyclic graphs are: (1) the problem under the vertex-disjoint paths mode can be approximated within a factor of O (log n / log OPT) of the optimum in O (mn log n)-time; (2) the problem under the edge-disjoint paths mode can be approximated within a factor of O (Δ* / log Δ*) of the optimum in O (mn log n)-time, where Δ* is the minimum k such that there is a spanning tree of the graph with maximum degree k. © 2007 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Algorithm
  • Directed acyclic graph
  • Minimum time broadcast
  • Spanning tree

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free