Approximation of Spanning Tree Congestion Using Hereditary Bisection

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Approximation of Spanning Tree Congestion Using Hereditary Bisection

Popis výsledku v původním jazyce

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) &gt;= Omega(hb(G)/Delta).

Název v anglickém jazyce

Approximation of Spanning Tree Congestion Using Hereditary Bisection

Popis výsledku anglicky

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) &gt;= Omega(hb(G)/Delta).

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)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název statě ve sborníku

42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

ISBN

978-3-95977-365-2

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

6

Strana od-do

63.1-63.6

Název nakladatele

Schloss Dagstuhl -- Leibniz-Zentrum f{&quot;u}r Informatik

Místo vydání

Dagstuhl, Germany

Místo konání akce

Jena

Datum konání akce

4. 3. 2025

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001532683200063