Parameterized approximation schemes for steiner trees with small number of Steiner vertices

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385829" target="_blank" >RIV/00216208:11320/18:10385829 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.STACS.2018.26" target="_blank" >https://doi.org/10.4230/LIPIcs.STACS.2018.26</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.STACS.2018.26" target="_blank" >10.4230/LIPIcs.STACS.2018.26</a>

Result language

angličtina

Original language name

Parameterized approximation schemes for steiner trees with small number of Steiner vertices

Original language description

We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This problem has been extensively studied from the viewpoint of approximation and also parametrization. In particular, on one hand Steiner Tree is known to be APX-hard, and W[2]-hard on the other, if parameterized by the number of non-terminals (Steiner vertices) in the optimum solution. In contrast to this we give an efficient parameterized approximation scheme (EPAS), which circumvents both hardness results. Moreover, our methods imply the existence of a polynomial size approximate kernelization scheme (PSAKS) for the considered parameter. We further study the parameterized approximability of other variants of Steiner Tree, such as Directed Steiner Tree and Steiner Forest. For neither of these an EPAS is likely to exist for the studied parameter: for Steiner Forest an easy observation shows that the problem is APX-hard, even if the input graph contains no Steiner vertices. For Directed Steiner Tree we prove that computing a constant approximation for this parameter is W[1]-hard. Nevertheless, we show that an EPAS exists for Unweighted Directed Steiner Tree. Also we prove that there is an EPAS and a PSAKS for Steiner Forest if in addition to the number of Steiner vertices, the number of connected components of an optimal solution is considered to be a parameter.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

35th Symposium on Theoretical Aspects of Computer Science, {STACS} 2018

ISBN

978-3-95977-062-0

ISSN

1868-8969

e-ISSN

neuvedeno

Number of pages

15

Pages from-to

1-15

Publisher name

Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

Place of publication

Schloss Dagstuhl, Germany

Event location

Caen, France

Event date

Feb 28, 2018

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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