Tree spanners for subgraphs and related tree covering problems

Dagmar Handke, Guy Kortsarz

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


For any fixed parameter k fi 1, a tree k-spanner of a graph G is a spanning tree T in G such that the distance between every pair of vertices in T is at most k times their distance in G. In this paper, we generalize on this very restrictive concept, and introduce Steiner tree k-spanners: We are given an input graph consisting of terminals and Steiner vertices, and we are now looking for a tree k-spanner that spans all terminals. The complexity status of deciding the existence of a Steiner tree k- spanner is easy for some k: it is NP-hard for k fi 4, and it is in P for k = 1. For the case k = 2, we develop a model in terms of an equivalent tree covering problem, and use this to show NP-hardness. By showing the NP-hardness also for the case k = 3, the complexity results for all k are complete. We also consider the problem of finding a smallest Steiner tree k-spanner (if one exists at all). For any arbitrary k fi 2, we prove that we cannot hope to find eficiently a Steiner tree k-spanner that is closer to the smallest one than within a logarithmic factor. We conclude by discussing some problems related to the model for the case k = 2.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 26th International Workshop, WG 2000 Konstanz, Germany, June 15-17, 2000 Proceedings
EditorsUlrik Brandes, Dorothea Wagner
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540411836
StatePublished - 2000
Event26th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2000 - Konstanz, Germany
Duration: 15 Jun 200017 Jun 2000

Publication series

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


Conference26th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2000

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.


Dive into the research topics of 'Tree spanners for subgraphs and related tree covering problems'. Together they form a unique fingerprint.

Cite this