IEICE TRANSACTIONS on Information
Dominating Sets and Induced Matchings in Orthogonal Ray Graphs
Summary :
An orthogonal ray graph is an intersection graph of horizontal and vertical rays (closed half-lines) in the plane. Such a graph is 3-directional if every vertical ray has the same direction, and 2-directional if every vertical ray has the same direction and every horizontal ray has the same direction. We derive some structural properties of orthogonal ray graphs, and based on these properties, we introduce polynomial-time algorithms that solve the dominating set problem, the induced matching problem, and the strong edge coloring problem for these graphs. We show that for 2-directional orthogonal ray graphs, the dominating set problem can be solved in O(n2 log5 n) time, the weighted dominating set problem can be solved in O(n4 log n) time, and the number of dominating sets of a fixed size can be computed in O(n6 log n) time, where n is the number of vertices in the graph. We also show that for 2-directional orthogonal ray graphs, the weighted induced matching problem and the strong edge coloring problem can be solved in O(n2+m log n) time, where m is the number of edges in the graph. Moreover, we show that for 3-directional orthogonal ray graphs, the induced matching problem can be solved in O(m2) time, the weighted induced matching problem can be solved in O(m4) time, and the strong edge coloring problem can be solved in O(m3) time. We finally show that the weighted induced matching problem can be solved in O(m6) time for orthogonal ray graphs.
- Publication
- IEICE TRANSACTIONS on Information Vol.E97-D No.12 pp.3101-3109
- Publication Date
- 2014/12/01
- Publicized
- 2014/09/09
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2014EDP7184
- Type of Manuscript
- PAPER
- Category
- Fundamentals of Information Systems
Authors
Asahi TAKAOKA
Tokyo Institute of Technology
Satoshi TAYU
Tokyo Institute of Technology
Shuichi UENO
Tokyo Institute of Technology
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Asahi TAKAOKA, Satoshi TAYU, Shuichi UENO, "Dominating Sets and Induced Matchings in Orthogonal Ray Graphs" in IEICE TRANSACTIONS on Information,
vol. E97-D, no. 12, pp. 3101-3109, December 2014, doi: 10.1587/transinf.2014EDP7184.
Abstract: An orthogonal ray graph is an intersection graph of horizontal and vertical rays (closed half-lines) in the plane. Such a graph is 3-directional if every vertical ray has the same direction, and 2-directional if every vertical ray has the same direction and every horizontal ray has the same direction. We derive some structural properties of orthogonal ray graphs, and based on these properties, we introduce polynomial-time algorithms that solve the dominating set problem, the induced matching problem, and the strong edge coloring problem for these graphs. We show that for 2-directional orthogonal ray graphs, the dominating set problem can be solved in O(n2 log5 n) time, the weighted dominating set problem can be solved in O(n4 log n) time, and the number of dominating sets of a fixed size can be computed in O(n6 log n) time, where n is the number of vertices in the graph. We also show that for 2-directional orthogonal ray graphs, the weighted induced matching problem and the strong edge coloring problem can be solved in O(n2+m log n) time, where m is the number of edges in the graph. Moreover, we show that for 3-directional orthogonal ray graphs, the induced matching problem can be solved in O(m2) time, the weighted induced matching problem can be solved in O(m4) time, and the strong edge coloring problem can be solved in O(m3) time. We finally show that the weighted induced matching problem can be solved in O(m6) time for orthogonal ray graphs.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2014EDP7184/_p
Copy
@ARTICLE{e97-d_12_3101,
author={Asahi TAKAOKA, Satoshi TAYU, Shuichi UENO, },
journal={IEICE TRANSACTIONS on Information},
title={Dominating Sets and Induced Matchings in Orthogonal Ray Graphs},
year={2014},
volume={E97-D},
number={12},
pages={3101-3109},
abstract={An orthogonal ray graph is an intersection graph of horizontal and vertical rays (closed half-lines) in the plane. Such a graph is 3-directional if every vertical ray has the same direction, and 2-directional if every vertical ray has the same direction and every horizontal ray has the same direction. We derive some structural properties of orthogonal ray graphs, and based on these properties, we introduce polynomial-time algorithms that solve the dominating set problem, the induced matching problem, and the strong edge coloring problem for these graphs. We show that for 2-directional orthogonal ray graphs, the dominating set problem can be solved in O(n2 log5 n) time, the weighted dominating set problem can be solved in O(n4 log n) time, and the number of dominating sets of a fixed size can be computed in O(n6 log n) time, where n is the number of vertices in the graph. We also show that for 2-directional orthogonal ray graphs, the weighted induced matching problem and the strong edge coloring problem can be solved in O(n2+m log n) time, where m is the number of edges in the graph. Moreover, we show that for 3-directional orthogonal ray graphs, the induced matching problem can be solved in O(m2) time, the weighted induced matching problem can be solved in O(m4) time, and the strong edge coloring problem can be solved in O(m3) time. We finally show that the weighted induced matching problem can be solved in O(m6) time for orthogonal ray graphs.},
keywords={},
doi={10.1587/transinf.2014EDP7184},
ISSN={1745-1361},
month={December},}
Copy
TY - JOUR
TI - Dominating Sets and Induced Matchings in Orthogonal Ray Graphs
T2 - IEICE TRANSACTIONS on Information
SP - 3101
EP - 3109
AU - Asahi TAKAOKA
AU - Satoshi TAYU
AU - Shuichi UENO
PY - 2014
DO - 10.1587/transinf.2014EDP7184
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E97-D
IS - 12
JA - IEICE TRANSACTIONS on Information
Y1 - December 2014
AB - An orthogonal ray graph is an intersection graph of horizontal and vertical rays (closed half-lines) in the plane. Such a graph is 3-directional if every vertical ray has the same direction, and 2-directional if every vertical ray has the same direction and every horizontal ray has the same direction. We derive some structural properties of orthogonal ray graphs, and based on these properties, we introduce polynomial-time algorithms that solve the dominating set problem, the induced matching problem, and the strong edge coloring problem for these graphs. We show that for 2-directional orthogonal ray graphs, the dominating set problem can be solved in O(n2 log5 n) time, the weighted dominating set problem can be solved in O(n4 log n) time, and the number of dominating sets of a fixed size can be computed in O(n6 log n) time, where n is the number of vertices in the graph. We also show that for 2-directional orthogonal ray graphs, the weighted induced matching problem and the strong edge coloring problem can be solved in O(n2+m log n) time, where m is the number of edges in the graph. Moreover, we show that for 3-directional orthogonal ray graphs, the induced matching problem can be solved in O(m2) time, the weighted induced matching problem can be solved in O(m4) time, and the strong edge coloring problem can be solved in O(m3) time. We finally show that the weighted induced matching problem can be solved in O(m6) time for orthogonal ray graphs.
ER -
English
