Approximation of Spanning Tree Congestion Using Hereditary Bisection

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10510123" target="_blank" >RIV/00216208:11320/25:10510123 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.STACS.2025.63" target="_blank" >https://doi.org/10.4230/LIPIcs.STACS.2025.63</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.STACS.2025.63" target="_blank" >10.4230/LIPIcs.STACS.2025.63</a>

Result language
angličtina
Original language name
Approximation of Spanning Tree Congestion Using Hereditary Bisection
Original language description
The Spanning Tree Congestion (STC) problem is the following NP-hard problem: given a graph G, construct a spanning tree T of G minimizing its maximum edge congestion where the congestion of an edge e is an element of T is the number of edges uv in G such that the unique path between u and v in T passes through e; the optimal value for a given graph G is denoted STC(G). It is known that every spanning tree is an n/2-approximation for the STC problem. A longstanding problem is to design a better approximation algorithm. Our contribution towards this goal is an O(Delta center dot log(3/2) n)-approximation algorithm where Delta is the maximum degree in G and n the number of vertices. For graphs with a maximum degree bounded by a polylog of the number of vertices, this is an exponential improvement over the previous best approximation. Our main tool for the algorithm is a new lower bound on the spanning tree congestion which is of independent interest. Denoting by hb(G) the hereditary bisection of G which is the maximum bisection width over all subgraphs of G, we prove that for every graph G, STC(G) >= Omega(hb(G)/Delta).
Czech name
—
Czech description
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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)

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)
ISBN
978-3-95977-365-2
ISSN
1868-8969
e-ISSN
—
Number of pages
6
Pages from-to
63.1-63.6
Publisher name
Schloss Dagstuhl -- Leibniz-Zentrum f{"u}r Informatik
Place of publication
Dagstuhl, Germany
Event location
Jena
Event date
Mar 4, 2025
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
001532683200063

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