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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Algorithmica

ISSN

0178-4617

e-ISSN

—

Svazek periodika

81

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

1031-1052

Kód UT WoS článku

000460105700005

EID výsledku v databázi Scopus

2-s2.0-85046896645