Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422373" target="_blank" >RIV/00216208:11320/20:10422373 - isvavai.cz</a>
Nalezeny alternativní kódy
RIV/68407700:21240/20:00345591
Výsledek na webu
<a href="https://doi.org/10.4230/LIPIcs.IPEC.2020.16" target="_blank" >https://doi.org/10.4230/LIPIcs.IPEC.2020.16</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.IPEC.2020.16" target="_blank" >10.4230/LIPIcs.IPEC.2020.16</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View
Popis výsledku v původním jazyce
In the Steiner Tree problem, we are given an edge-weighted undirected graph G = (V,E) and a set of terminals R SUBSET OF OR EQUAL TO V. The task is to find a connected subgraph of G containing R and minimizing the sum of weights of its edges. Steiner Tree is well known to be NP-complete and is undoubtedly one of the most studied problems in (applied) computer science. We observe that many approximation algorithms for Steiner Tree follow a similar scheme (meta-algorithm) and perform (exhaustively) a similar routine which we call star contraction. Here, by a star contraction, we mean finding a star-like subgraph in (the metric closure of) the input graph minimizing the ratio of its weight to the number of contained terminals minus one; and contract. It is not hard to see that the well-known MST-approximation seeks the best star to contract among those containing two terminals only. Zelikovsky's approximation algorithm follows a similar workflow, finding the best star among those containing three terminals. We perform an empirical study of star contractions with the relaxed condition on the number of terminals in each star contraction motivated by a recent result of Dvořák et al. [Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices, STACS 2018]. Furthermore, we propose two improvements of Zelikovsky's 11/6-approximation algorithm and we empirically confirm that the quality of the solution returned by any of these is better than the one returned by the former algorithm. However, such an improvement is exchanged for a slower running time (up to a multiplicative factor of the number of terminals).
Název v anglickém jazyce
Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View
Popis výsledku anglicky
In the Steiner Tree problem, we are given an edge-weighted undirected graph G = (V,E) and a set of terminals R SUBSET OF OR EQUAL TO V. The task is to find a connected subgraph of G containing R and minimizing the sum of weights of its edges. Steiner Tree is well known to be NP-complete and is undoubtedly one of the most studied problems in (applied) computer science. We observe that many approximation algorithms for Steiner Tree follow a similar scheme (meta-algorithm) and perform (exhaustively) a similar routine which we call star contraction. Here, by a star contraction, we mean finding a star-like subgraph in (the metric closure of) the input graph minimizing the ratio of its weight to the number of contained terminals minus one; and contract. It is not hard to see that the well-known MST-approximation seeks the best star to contract among those containing two terminals only. Zelikovsky's approximation algorithm follows a similar workflow, finding the best star among those containing three terminals. We perform an empirical study of star contractions with the relaxed condition on the number of terminals in each star contraction motivated by a recent result of Dvořák et al. [Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices, STACS 2018]. Furthermore, we propose two improvements of Zelikovsky's 11/6-approximation algorithm and we empirically confirm that the quality of the solution returned by any of these is better than the one returned by the former algorithm. However, such an improvement is exchanged for a slower running time (up to a multiplicative factor of the number of terminals).
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
<a href="/cs/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Výzkumné centrum informatiky</a><br>
Návaznosti
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2020
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
15th International Symposium on Parameterized and Exact Computation, (IPEC 2020)
ISBN
978-3-95977-172-6
ISSN
1868-8969
e-ISSN
—
Počet stran výsledku
18
Strana od-do
1-18
Název nakladatele
Schloss Dagstuhl--Leibniz-Zentrum für Informatik
Místo vydání
Dagstuhl, Germany
Místo konání akce
Hong Kong
Datum konání akce
14. 12. 2020
Typ akce podle státní příslušnosti
WRD - Celosvětová akce
Kód UT WoS článku
—