Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, September 22, 2015, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Yoshio Okamoto (University of Electro-Communications Tokyo)

Minimum-Cost b-Edge Dominating Sets on Trees

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 linear-programming 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.

This is joint work with Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama and Yusuke Kobayashi.

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