TY - CONF

T1 - Bottleneck bichromatic full steiner trees

AU - Karim Abu-Affash, A.

AU - Bhore, Sujoy

AU - Carmi, Paz

AU - Chakraborty, Dibyayan

N1 - Funding Information:
†Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel, sujoy.bhore@gmail.com. The research is partially supported by the Lynn and William Frankel Center for Computer Science.
Funding Information:
‡Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel, carmip@cs.bgu.ac.il. The research is partially supported by the Lynn and William Frankel Center for Computer Science.
Publisher Copyright:
Compilation copyright © 2017 Michiel Smid Copyright of individual papers retained by authors.All right reserved.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Given two sets of points in the plane, Q of n (terminal) points and S of m (Steiner) points, where each of Q and S contains bichromatic points (red and blue points), a full bichromatic Steiner tree is a Steiner tree in which all points of Q are leaves and each edge of the tree is bichromatic (i.e., connects a red and a blue point). In the bottleneck bichromatic full Steiner tree (BBFST) problem, the goal is to compute a bichromatic full Steiner tree T, such that the length of the longest edge in T is minimized. In k-BBFST problem, the goal is to find a bichromatic full Steiner tree T with at most k ≤ m Steiner points from S, such that the length of the longest edge in T is minimized. In this paper, we present an O((n + m) log m) time algorithm that solves the BBFST problem. Moreover, we show that k-BBFST problem is NP-hard and we give a polynomial-time 9-approximation algorithm for the problem.

AB - Given two sets of points in the plane, Q of n (terminal) points and S of m (Steiner) points, where each of Q and S contains bichromatic points (red and blue points), a full bichromatic Steiner tree is a Steiner tree in which all points of Q are leaves and each edge of the tree is bichromatic (i.e., connects a red and a blue point). In the bottleneck bichromatic full Steiner tree (BBFST) problem, the goal is to compute a bichromatic full Steiner tree T, such that the length of the longest edge in T is minimized. In k-BBFST problem, the goal is to find a bichromatic full Steiner tree T with at most k ≤ m Steiner points from S, such that the length of the longest edge in T is minimized. In this paper, we present an O((n + m) log m) time algorithm that solves the BBFST problem. Moreover, we show that k-BBFST problem is NP-hard and we give a polynomial-time 9-approximation algorithm for the problem.

UR - http://www.scopus.com/inward/record.url?scp=85072837963&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85072837963

SP - 13

EP - 18

T2 - 29th Canadian Conference on Computational Geometry, CCCG 2017

Y2 - 26 July 2017 through 28 July 2017

ER -