Generating low-degree 2-spanners

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

This research was supported in part by a Walter and Abstract. A k-spanner of a connected (undirected unweighted) graph G = (V, E) is a subgraph G' consisting of all the vertices of V and a subset of the edges, with the additional property that the distance between any two vertices in G' is larger than that distance in G by no more than a factor of k. This paper is concerned with approximating the problem of finding a 2-spanner in a given graph, with minimum maximum degree. We first show that the problem is at least as hard to approximate as set cover. Then a randomized approximation algorithm is provided for this problem, with approximation ratio of Õ(Δ1/4). We then present a probabilistic algorithm that is more efficient for sparse graphs. Our algorithms are converted into deterministic ones using derandomization.

Original language English (US) 1438-1456 19 SIAM Journal on Computing 27 5 https://doi.org/10.1137/S0097539794268753 Published - Jan 1 1998 Yes

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Spanners
Spanner
Approximation algorithms
Derandomization
Probabilistic Algorithms
Set Cover
Sparse Graphs
Randomized Algorithms
Maximum Degree
Undirected Graph
Connected graph
Approximation Algorithms
Subgraph
Subset
Approximation
Graph in graph theory

All Science Journal Classification (ASJC) codes

• Mathematics(all)
• Computer Science(all)

Cite this

Kortsarz, Guy. / Generating low-degree 2-spanners. In: SIAM Journal on Computing. 1998 ; Vol. 27, No. 5. pp. 1438-1456.
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In: SIAM Journal on Computing, Vol. 27, No. 5, 01.01.1998, p. 1438-1456.

Research output: Contribution to journalArticle

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