Minimum-cost b-Edge dominating sets on trees

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish
Title of host publicationAlgorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
EditorsHee-Kap Ahn, Chan-Su Shin
PublisherSpringer Verlag
Pages195-207
Number of pages13
ISBN (Electronic)9783319130743
DOIs
Publication statusPublished - Jan 1 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8889
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Fingerprint

Dominating Set
Polynomials
Costs
Polynomial-time Algorithm
Computational complexity
Open Problems
Leaves
Trees (mathematics)
Fully Polynomial Time Approximation Scheme
Linear programming
Fixed-parameter Algorithms
Path
Combinatorial Algorithms
NP-hardness
Hardness
Best Approximation
Computational Complexity
NP-complete problem
Alternatives

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ito, T., Kakimura, N., Kamiyama, N., Kobayashi, Y., & Okamoto, Y. (2014). Minimum-cost b-Edge dominating sets on trees. In H-K. Ahn, & C-S. Shin (Eds.), Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings (pp. 195-207). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8889). Springer Verlag. https://doi.org/10.1007/978-3-319-13075-0_16

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. ed. / Hee-Kap Ahn; Chan-Su Shin. 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 proceedingChapter

Ito, T, Kakimura, N, Kamiyama, N, Kobayashi, Y & Okamoto, Y 2014, Minimum-cost b-Edge dominating sets on trees. in H-K Ahn & C-S Shin (eds), Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8889, Springer Verlag, pp. 195-207. https://doi.org/10.1007/978-3-319-13075-0_16
Ito T, Kakimura N, Kamiyama N, Kobayashi Y, Okamoto Y. Minimum-cost b-Edge dominating sets on trees. In Ahn H-K, Shin C-S, editors, Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings. Springer Verlag. 2014. p. 195-207. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-13075-0_16
Ito, Takehiro ; Kakimura, Naonori ; Kamiyama, Naoyuki ; Kobayashi, Yusuke ; Okamoto, Yoshio. / Minimum-cost b-Edge dominating sets on trees. Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings. editor / Hee-Kap Ahn ; Chan-Su Shin. Springer Verlag, 2014. pp. 195-207 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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