Abstract
We consider the minimum-cost b-edge dominating set problem. This is a generalization of the edge dominating set problem, but the computational complexity for trees is an astonishing open problem. We make steps toward the resolution of this open problem in the following three directions. (1) We give the first combinatorial polynomial-time algorithm for paths. Prior to our work, the polynomial-time algorithm for paths used linear programming, and it was known that the linearprogramming approach could not be extended to trees. Thus, our algorithm would yield an alternative approach to a possible polynomial-time algorithm for trees. (2) We give a fixed-parameter algorithm for trees with the number of leaves as a parameter. Thus, a possible NP-hardness proof for trees should make use of trees with unbounded number of leaves. (3) We give a fully polynomial-time approximation scheme for trees. Prior to our work, the best known approximation factor was two. If the problem is NP-hard, then a possible proof cannot be done via a gap-preserving reduction from any APX-hard problem unless P = NP.
| Original language | English |
|---|---|
| Title of host publication | Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings |
| Publisher | Springer Verlag |
| Pages | 195-207 |
| Number of pages | 13 |
| Volume | 8889 |
| ISBN (Electronic) | 9783319130743 |
| DOIs | |
| Publication status | Published - 2014 |
| Externally published | Yes |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 8889 |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
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ASJC Scopus subject areas
- Computer Science(all)
- Theoretical Computer Science
Cite this
Minimum-cost b-Edge dominating sets on trees. / Ito, Takehiro; Kakimura, Naonori; Kamiyama, Naoyuki; Kobayashi, Yusuke; Okamoto, Yoshio.
Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings. Vol. 8889 Springer Verlag, 2014. p. 195-207 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8889).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - Minimum-cost b-Edge dominating sets on trees
AU - Ito, Takehiro
AU - Kakimura, Naonori
AU - Kamiyama, Naoyuki
AU - Kobayashi, Yusuke
AU - Okamoto, Yoshio
PY - 2014
Y1 - 2014
N2 - We consider the minimum-cost b-edge dominating set problem. This is a generalization of the edge dominating set problem, but the computational complexity for trees is an astonishing open problem. We make steps toward the resolution of this open problem in the following three directions. (1) We give the first combinatorial polynomial-time algorithm for paths. Prior to our work, the polynomial-time algorithm for paths used linear programming, and it was known that the linearprogramming approach could not be extended to trees. Thus, our algorithm would yield an alternative approach to a possible polynomial-time algorithm for trees. (2) We give a fixed-parameter algorithm for trees with the number of leaves as a parameter. Thus, a possible NP-hardness proof for trees should make use of trees with unbounded number of leaves. (3) We give a fully polynomial-time approximation scheme for trees. Prior to our work, the best known approximation factor was two. If the problem is NP-hard, then a possible proof cannot be done via a gap-preserving reduction from any APX-hard problem unless P = NP.
AB - We consider the minimum-cost b-edge dominating set problem. This is a generalization of the edge dominating set problem, but the computational complexity for trees is an astonishing open problem. We make steps toward the resolution of this open problem in the following three directions. (1) We give the first combinatorial polynomial-time algorithm for paths. Prior to our work, the polynomial-time algorithm for paths used linear programming, and it was known that the linearprogramming approach could not be extended to trees. Thus, our algorithm would yield an alternative approach to a possible polynomial-time algorithm for trees. (2) We give a fixed-parameter algorithm for trees with the number of leaves as a parameter. Thus, a possible NP-hardness proof for trees should make use of trees with unbounded number of leaves. (3) We give a fully polynomial-time approximation scheme for trees. Prior to our work, the best known approximation factor was two. If the problem is NP-hard, then a possible proof cannot be done via a gap-preserving reduction from any APX-hard problem unless P = NP.
UR - http://www.scopus.com/inward/record.url?scp=84921656602&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84921656602&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-13075-0_16
DO - 10.1007/978-3-319-13075-0_16
M3 - Chapter
AN - SCOPUS:84921656602
VL - 8889
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 195
EP - 207
BT - Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
PB - Springer Verlag
ER -