On the Internal Steiner Tree Problem

Hsieh, Sun-Yuan; Gao, Huang-Ming; Yang, Shih-Cheng

doi:10.1007/978-3-540-72504-6_25

Cited by 3 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This problem can be viewed as a reverse problem of PTSTP. As a reverse problem of TSTP, Heish et.al [6] presented internal Steiner tree problem (ISTP). Given a weighted complete graph G = (V, E; w) and a terminal set R V with | V \ R | 2, the ISTP is to find a minimum sub-tree T of G interconnecting R such that all vertices of R are not leaves of T .…”

Section: Introductionmentioning

confidence: 99%

The relationship among some variables of Steiner tree problem

Zhao

2012

2012 IEEE Symposium on Robotics and Applications (ISRA)

View full text Add to dashboard Cite

Given a weighted complete graph G = (V, E; w) and a subset R V, the Steiner tree problem (STP) is to find a minimum sub-tree of G interconnecting R. In this paper, we consider the relationship among the following 4 variables of STP: terminal Steiner tree problem (TSTP), partial-terminal Steiner tree problem (PTSTP), internal Steiner tree problem (ISTP) and selected-internal Steiner tree problem (SISTP). Firstly, we show that if SISTP has an approximation problem with approximation ratio , then ISTP also has an approximation algorithm with the same ratio. Then, we prove that the same result holds between PTSTP and TSTP.

show abstract

Section: Introductionmentioning

confidence: 99%

The relationship among some variables of Steiner tree problem

Zhao

2012

2012 IEEE Symposium on Robotics and Applications (ISRA)

View full text Add to dashboard Cite

show abstract

An Efficient Approximation Algorithm for the Steiner Tree Problem

Chen¹,

Hsieh²

2020

Complexity and Approximation

Self Cite

View full text Add to dashboard Cite

The Steiner tree problem is one of the classic and most fundamental N P-hard problems: given an arbitrary weighted graph, seek a minimum-cost tree spanning a given subset of the vertices (terminals). Byrka et al. proposed a 1.3863 + -approximation algorithm in which the linear program is solved at every iteration after contracting a component. Goemans et al. shown that it is possible to achieve the same approximation guarantee while only solving hypergraphic LP relaxation once. However, optimizing hypergraphic LP relaxation exactly is strongly NPhard. This article presents an efficient two-phase heuristic in greedy strategy that achieves an approximation ratio of 1.4295.

show abstract

Algorithms for the minimum diameter terminal Steiner tree problem

Ding

Qiu

2013

J Comb Optim

View full text Add to dashboard Cite

On the Internal Steiner Tree Problem

Cited by 3 publications

References 7 publications

The relationship among some variables of Steiner tree problem

The relationship among some variables of Steiner tree problem

An Efficient Approximation Algorithm for the Steiner Tree Problem

Algorithms for the minimum diameter terminal Steiner tree problem

Contact Info

Product

Resources

About