# Bottleneck bichromatic full Steiner trees

## Article Type

Research Article

## Publication Title

Information Processing Letters

## Abstract

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 the 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 first present an O((n+m)logm) time algorithm that solves the BBFST problem. Then, we show that k-BBFST problem is NP-hard and cannot be approximated within a factor of 5 in polynomial time, unless P=NP. Finally, we give a polynomial-time 9-approximation algorithm for the k-BBFST problem.

## First Page

14

## Last Page

19

## DOI

10.1016/j.ipl.2018.10.003

## Publication Date

2-1-2019

## Recommended Citation

Abu-Affash, A. Karim; Bhore, Sujoy; Carmi, Paz; and Chakraborty, Dibyayan, "Bottleneck bichromatic full Steiner trees" (2019). *Journal Articles*. 970.

https://digitalcommons.isical.ac.in/journal-articles/970