Max-stretch reduction for tree spanners
(2005) 9th International Workshop, WADS 2005 3608. p.122-133- 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... (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 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/220496
- author
- Iwama, K ; Lingas, Andrzej LU and Okita, M
- organization
- publishing date
- 2005
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Algorithms and Data Structures / Lecture Notes in Computer Science
- volume
- 3608
- pages
- 122 - 133
- publisher
- Springer
- conference name
- 9th International Workshop, WADS 2005
- conference location
- Waterloo, Canada
- conference dates
- 2005-08-15 - 2005-08-17
- external identifiers
-
- wos:000231873500012
- scopus:26844486244
- ISSN
- 0302-9743
- 1611-3349
- ISBN
- 978-3-540-28101-6
- DOI
- 10.1007/11534273
- project
- VR 2002-4049
- language
- English
- LU publication?
- yes
- id
- 9057d95e-64b8-4fb9-88c9-75809aadded9 (old id 220496)
- date added to LUP
- 2016-04-01 12:08:15
- date last changed
- 2024-01-08 09:42:27
@inproceedings{9057d95e-64b8-4fb9-88c9-75809aadded9,
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 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, K and Lingas, Andrzej and Okita, M}},
booktitle = {{Algorithms and Data Structures / Lecture Notes in Computer Science}},
isbn = {{978-3-540-28101-6}},
issn = {{0302-9743}},
language = {{eng}},
pages = {{122--133}},
publisher = {{Springer}},
title = {{Max-stretch reduction for tree spanners}},
url = {{http://dx.doi.org/10.1007/11534273}},
doi = {{10.1007/11534273}},
volume = {{3608}},
year = {{2005}},
}