DMCA
Additive Spanners and (α, β)-Spanners
| Citations: | 14 - 3 self |
BibTeX
@MISC{Baswana_additivespanners,
author = {Surender Baswana and Telikepalli Kavitha and Kurt Mehlhorn and Seth Pettie},
title = {Additive Spanners and (α, β)-Spanners },
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
An (α, β)-spanner of an unweighted graph G is a subgraph H that distorts distances in G up to a multiplicative factor of α and an additive term β. It is well known that any graph contains a (multiplicative) (2k − 1, 0)-spanner of size O(n 1+1/k) and an (additive) (1, 2)-spanner of size O(n 3/2). However no other additive spanners are known to exist. In this paper we develop a couple of new techniques for constructing (α, β)-spanners. Our first result is an additive (1, 6)-spanner of size O(n 4/3). The construction algorithm can be understood as an economical agent that assigns costs and values to paths in the graph, purchasing affordable paths and ignoring expensive ones, which are intuitively well-approximated by paths already purchased. We show that this path buying algorithm can be parameterized in different ways to yield other sparseness-distortion tradeoffs. Our second result addresses the problem of which (α, β)-spanners can be computed efficiently, ideally in linear time. We show that for any k, a (k, k − 1)-spanner with size O(kn 1+1/k) can be found in linear time, and further, that in a distributed network the algorithm terminates in a constant number of rounds. Previous spanner constructions with similar performance had roughly twice the multiplicative distortion.
Keyphrases
additive spanner linear time constant number new technique second result unweighted graph similar performance distributed network construction algorithm sparseness-distortion tradeoff previous spanner construction different way expensive one economical agent multiplicative distortion affordable path first result multiplicative factor additive term
