Fixed-Parameter Approximations for k-Center Problems in Low Highway Dimension Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10403063" target="_blank" >RIV/00216208:11320/19:10403063 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=-aGNgvm9XI" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=-aGNgvm9XI</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00453-018-0455-0" target="_blank" >10.1007/s00453-018-0455-0</a>

Result language

angličtina

Original language name

Fixed-Parameter Approximations for k-Center Problems in Low Highway Dimension Graphs

Original language description

We consider the k-Center problem and some generalizations. For k-Center a set of kcenter vertices needs to be found in a graph G with edge lengths, such that the distance from any vertex ofG to its nearest center is minimized. This problem naturally occurs in transportation networks, and therefore we model the inputs as graphs with bounded highway dimension, as proposed by Abraham etal. (SODA, pp 782-793, 2010). We show both approximation and fixed-parameter hardness results, and how to overcome them using fixed-parameter approximations, where the two paradigms are combined. In particular, we prove that for any epsilon&gt;0 computing a (2-epsilon)-approximation is W[2]-hard for parameterk, and NP-hard for graphs with highway dimension O(log2n). The latter does not rule out fixed-parameter (2-epsilon)-approximations for the highway dimension parameterh, but implies that such an algorithm must have at least doubly exponential running time in h if it exists, unless ETH fails. On the positive side, we show how to get below the approximation factor of2 by combining the parameters k andh: we develop a fixed-parameter 3/2-approximation with running time 2O(khlogh)&lt;bold&gt;nO&lt;/bold&gt;(1). Additionally we prove that, unless P=NP, our techniques cannot be used to compute fixed-parameter (2-epsilon)-approximations for only the parameter h. We also provide similar fixed-parameter approximations for the weightedk-Center and (k,F)-Partition problems, which generalize k-Center.

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

<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

Continuities

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

Publication year

2019

Confidentiality

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

Name of the periodical

Algorithmica

ISSN

0178-4617

e-ISSN

—

Volume of the periodical

81

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

22

Pages from-to

1031-1052

UT code for WoS article

000460105700005

EID of the result in the Scopus database

2-s2.0-85046896645