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%2F21%3A10437488" target="_blank" >RIV/00216208:11320/21:10437488 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21240/21:00349869

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=MpXW6cCZYS" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=MpXW6cCZYS</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/18M1209489" target="_blank" >10.1137/18M1209489</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 parameterization. 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 nonterminals (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 none of these is an EPAS 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 approximating within any function of the studied parameter is W[1]-hard. Nevertheless, we show that an EPAS exists for Unweighted Directed Steiner Tree, but a PSAKS does not. We also 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

J_imp - Article in a specialist periodical, which is included in the Web of Science database

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

2021

Confidentiality

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

Name of the periodical

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

—

Volume of the periodical

35

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

29

Pages from-to

546-574

UT code for WoS article

000636039400029

EID of the result in the Scopus database

2-s2.0-85105114337