Approximating the minimum degree spanning tree to within one from the optimal degree

Martin Fürer, Balaji Raghavachari

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

We consider the problem of constructing a spanning tree for a graph G = (V, E) with n vertices whose maximal degree is the smallest among all spanning trees of G. This problem is easily shown to be NP-haxd. We describe an iterative polynomial time approximation algorithm for this problem. This algorithm computes a spanning tree whose maximal degree is at most O(Delta;z.ast; +log n), where Δz.ast; is the degree of some optimal tree. The result is generalized to the case where only some vertices need to be connected (Steiner case) and to the case of directed graphs. It is then shown that our algorithm can be refined to produce a spanning tree of degree at most Δz.st; + 1. Unless P = NP, this is the best bound achievable in polynomial time.

Original languageEnglish (US)
Title of host publicationProceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
PublisherAssociation for Computing Machinery
Pages317-324
Number of pages8
ISBN (Electronic)089791466X
StatePublished - Sep 1 1992
Event3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 - Orlando, United States
Duration: Jan 27 1992Jan 29 1992

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
VolumePart F129721

Other

Other3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
Country/TerritoryUnited States
CityOrlando
Period1/27/921/29/92

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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