Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View
The result's identifiers
Result code in 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>
Alternative codes found
RIV/68407700:21240/20:00345591
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View
Original language description
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).
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
15th International Symposium on Parameterized and Exact Computation, (IPEC 2020)
ISBN
978-3-95977-172-6
ISSN
1868-8969
e-ISSN
—
Number of pages
18
Pages from-to
1-18
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum für Informatik
Place of publication
Dagstuhl, Germany
Event location
Hong Kong
Event date
Dec 14, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—