@inproceedings{447cad7fd7c245be8f1519267d15e88b,

title = "Approximating Steiner trees and forests with minimum number of Steiner points",

abstract = "Let R be a finite set of terminals in a metric space (M,d). We consider finding a minimum size set S ⊆ M of additional points such that the unit-disc graph G[R ∪ S] of R ∪ S satisfies some connectivity properties. In the Steiner Tree with Minimum Number of Steiner Points (ST-MSP) problem G[R ∪ S] should be connected. In the more general Steiner Forest with Minimum Number of Steiner Points (SF-MSP) problem we are given a set D ⊆ R × R of demand pairs and G[R ∪ S] should contains a uv-path for every uv ∈ D. Let Δ be the maximum number of points in a unit ball such that the distance between any two of them is larger than 1. It is known that Δ = 5 in ℝ2. The previous known approximation ratio for ST-MSP was ⌊(Δ+1)/2⌋ +1+ϵ in an arbitrary normed space [15], and 2.5+ϵ in the Euclidean space ℝ2 [5]. Our approximation ratio for ST-MSP is 1+ln(Δ−1)+ϵ in an arbitrary normed space, which in ℝ2 reduces to 1+ln4+ϵ < 2.3863+ϵ. For SF-MSP we give a simple Δ- approximation algorithm, improving the folklore ratio 2(Δ−1). Finally, we generalize and simplify the Δ-approximation of Calinescu [3] for the 2-Connectivity-MSP problem, where G[R ∪ S] should be 2-connected.",

keywords = "2-connectivity, Approximation algorithms, Steiner forest, Steiner tree, Unit-disc graph, Wireless network",

author = "Nachshon Cohen and Zeev Nutov",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 12th International Workshop on Approximation and Online Algorithms, WAOA 2014 ; Conference date: 11-09-2014 Through 12-09-2014",

year = "2015",

doi = "https://doi.org/10.1007/978-3-319-18263-6_9",

language = "الإنجليزيّة",

isbn = "9783319182629",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "95--106",

editor = "Ola Svensson and Evripidis Bampis",

booktitle = "Approximation and Online Algorithms - 12th International Workshop, WAOA 2014, Revised Selected Papers",

}