The Euclidean Bottleneck Full Steiner Tree Problem

A. Karim Abu-Affash

doi:10.1007/s00453-013-9788-x

The Euclidean Bottleneck Full Steiner Tree Problem

A. Karim Abu-Affash

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Given two sets in the plane, R of n (terminal) points and S of m (Steiner) points, a full Steiner tree is a Steiner tree in which all points of R are leaves. In the bottleneck full Steiner tree (BFST) problem, one has to find a full Steiner tree T (with any number of Steiner points from S), such that the length of the longest edge in T is minimized, and, in the k-BFST problem, has to find a 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. The problems are motivated by wireless network design.

In this paper, we present an exact algorithm of (Formula presented.)time to solve the BFST problem. Moreover, we show that the k-BFST problem is NP-hard and that there exists a polynomial-time approximation algorithm for the problem with performance ratio 4.

Original language	English
Pages (from-to)	139-151
Number of pages	13
Journal	Algorithmica
Volume	71
Issue number	1
DOIs	https://doi.org/10.1007/s00453-013-9788-x
State	Published - 1 Jan 2015
Externally published	Yes

Keywords

Approximation algorithms
Bottleneck full Steiner tree problem
Geometric optimization
NP-hard
Steiner trees

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

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10.1007/s00453-013-9788-x

Cite this

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title = "The Euclidean Bottleneck Full Steiner Tree Problem",

abstract = "Given two sets in the plane, R of n (terminal) points and S of m (Steiner) points, a full Steiner tree is a Steiner tree in which all points of R are leaves. In the bottleneck full Steiner tree (BFST) problem, one has to find a full Steiner tree T (with any number of Steiner points from S), such that the length of the longest edge in T is minimized, and, in the k-BFST problem, has to find a 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. The problems are motivated by wireless network design.In this paper, we present an exact algorithm of (Formula presented.)time to solve the BFST problem. Moreover, we show that the k-BFST problem is NP-hard and that there exists a polynomial-time approximation algorithm for the problem with performance ratio 4.",

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N2 - Given two sets in the plane, R of n (terminal) points and S of m (Steiner) points, a full Steiner tree is a Steiner tree in which all points of R are leaves. In the bottleneck full Steiner tree (BFST) problem, one has to find a full Steiner tree T (with any number of Steiner points from S), such that the length of the longest edge in T is minimized, and, in the k-BFST problem, has to find a 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. The problems are motivated by wireless network design.In this paper, we present an exact algorithm of (Formula presented.)time to solve the BFST problem. Moreover, we show that the k-BFST problem is NP-hard and that there exists a polynomial-time approximation algorithm for the problem with performance ratio 4.

AB - Given two sets in the plane, R of n (terminal) points and S of m (Steiner) points, a full Steiner tree is a Steiner tree in which all points of R are leaves. In the bottleneck full Steiner tree (BFST) problem, one has to find a full Steiner tree T (with any number of Steiner points from S), such that the length of the longest edge in T is minimized, and, in the k-BFST problem, has to find a 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. The problems are motivated by wireless network design.In this paper, we present an exact algorithm of (Formula presented.)time to solve the BFST problem. Moreover, we show that the k-BFST problem is NP-hard and that there exists a polynomial-time approximation algorithm for the problem with performance ratio 4.

KW - Approximation algorithms

KW - Bottleneck full Steiner tree problem

KW - Geometric optimization

KW - NP-hard

KW - Steiner trees

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The Euclidean Bottleneck Full Steiner Tree Problem

Abstract

Keywords

ASJC Scopus subject areas

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