Max-stretch reduction for tree spanners
(2008) In Algorithmica 50(2). p.223-235- Abstract
- A tree t-spanner T of a graph G is a spanning tree of G whose max-stretch is t, i.e., the distance between any two vertices in T is at most t times their distance in G. If G has a tree t-spanner but not a tree (t−1)-spanner, then G is said to have max-stretch of t. In this paper, we study the Max-Stretch Reduction Problem: for an unweighted graph G=(V,E), find a set of edges not in E originally whose insertion into G can decrease the max-stretch of G. Our results are as follows: (i) For a ring graph, we give a linear-time algorithm which inserts k edges improving the max-stretch optimally. (ii) For a grid graph, we give a nearly optimal max-stretch reduction algorithm which preserves the structure of the grid. (iii) In the general case, we... (More)
- A tree t-spanner T of a graph G is a spanning tree of G whose max-stretch is t, i.e., the distance between any two vertices in T is at most t times their distance in G. If G has a tree t-spanner but not a tree (t−1)-spanner, then G is said to have max-stretch of t. In this paper, we study the Max-Stretch Reduction Problem: for an unweighted graph G=(V,E), find a set of edges not in E originally whose insertion into G can decrease the max-stretch of G. Our results are as follows: (i) For a ring graph, we give a linear-time algorithm which inserts k edges improving the max-stretch optimally. (ii) For a grid graph, we give a nearly optimal max-stretch reduction algorithm which preserves the structure of the grid. (iii) In the general case, we show that it is $mathcal{NP}$ -hard to decide, for a given graph G and its spanning tree of max-stretch t, whether or not one-edge insertion can decrease the max-stretch to t−1. (iv) Finally, we show that the max-stretch of an arbitrary graph on n vertices can be reduced to s′≥2 by inserting O(n/s′) edges, which can be determined in linear time, and observe that this number of edges is optimal up to a constant. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/629545
- author
- Iwama, Kazuo ; Lingas, Andrzej LU and Okita, Masaki
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Algorithmica
- volume
- 50
- issue
- 2
- pages
- 223 - 235
- publisher
- Springer
- external identifiers
-
- wos:000252190700004
- scopus:38149111914
- ISSN
- 0178-4617
- DOI
- 10.1007/s00453-007-9058-x
- project
- VR 2005-4085
- language
- English
- LU publication?
- yes
- id
- 9521794f-f6ba-4f82-8fc8-6cef334ce517 (old id 629545)
- date added to LUP
- 2016-04-01 12:22:04
- date last changed
- 2022-01-27 02:48:36
@article{9521794f-f6ba-4f82-8fc8-6cef334ce517,
abstract = {{A tree t-spanner T of a graph G is a spanning tree of G whose max-stretch is t, i.e., the distance between any two vertices in T is at most t times their distance in G. If G has a tree t-spanner but not a tree (t−1)-spanner, then G is said to have max-stretch of t. In this paper, we study the Max-Stretch Reduction Problem: for an unweighted graph G=(V,E), find a set of edges not in E originally whose insertion into G can decrease the max-stretch of G. Our results are as follows: (i) For a ring graph, we give a linear-time algorithm which inserts k edges improving the max-stretch optimally. (ii) For a grid graph, we give a nearly optimal max-stretch reduction algorithm which preserves the structure of the grid. (iii) In the general case, we show that it is $mathcal{NP}$ -hard to decide, for a given graph G and its spanning tree of max-stretch t, whether or not one-edge insertion can decrease the max-stretch to t−1. (iv) Finally, we show that the max-stretch of an arbitrary graph on n vertices can be reduced to s′≥2 by inserting O(n/s′) edges, which can be determined in linear time, and observe that this number of edges is optimal up to a constant.}},
author = {{Iwama, Kazuo and Lingas, Andrzej and Okita, Masaki}},
issn = {{0178-4617}},
language = {{eng}},
number = {{2}},
pages = {{223--235}},
publisher = {{Springer}},
series = {{Algorithmica}},
title = {{Max-stretch reduction for tree spanners}},
url = {{http://dx.doi.org/10.1007/s00453-007-9058-x}},
doi = {{10.1007/s00453-007-9058-x}},
volume = {{50}},
year = {{2008}},
}