Spanners of bounded degree graphs

Authors:
Fedor V. Fomin;Petr A. Golovach;Erik Jan Van Leeuwen
Affiliations:
Department of Informatics, University of Bergen, PB 7803, N-5020 Bergen, Norway;School of Engineering and Computing Sciences, Durham University, South Road, Durham DH1 3LE, UK;Department of Informatics, University of Bergen, PB 7803, N-5020 Bergen, Norway
Venue:
Information Processing Letters
Year:
2011

Citing 15
Cited 0

An optimal synchronizer for the hypercube

SIAM Journal on Computing
The monadic second-order logic of graphs. I. recognizable sets of finite graphs

Information and Computation
A special planar satisfiability problem and a consequence of its NP-completeness

Discrete Applied Mathematics
Tree Spanners

SIAM Journal on Discrete Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth

SIAM Journal on Computing
Tree spanners in planar graphs

Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Competitive concurrent distributed queuing

Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Low Stretch Spanning Trees

MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximating Minimum Max-Stretch spanning Trees on unweighted graphs

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)

Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Lower-Stretch Spanning Trees

SIAM Journal on Computing
A PTAS for the Sparsest Spanners Problem on Apex-Minor-Free Graphs

MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Nearly Tight Low Stretch Spanning Trees

FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Complexity results for the spanning tree congestion problem

WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science

Quantified Score

Hi-index	0.89

Visualization

Abstract

A k-spanner of a graph G is a spanning subgraph of G in which the distance between any pair of vertices is at most k times the distance in G. We prove that for fixed k,w, the problem of deciding if a given graph has a k-spanner of treewidth w is fixed-parameter tractable on graphs of bounded degree. In particular, this implies that finding a k-spanner that is a tree (a tree k-spanner) is fixed-parameter tractable on graphs of bounded degree. In contrast, we observe that if the graph has only one vertex of unbounded degree, then Treek-Spanner is NP-complete for k=4.