Streaming Algorithms for Geometric Steiner Forest

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455634" target="_blank" >RIV/00216208:11320/22:10455634 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.ICALP.2022.47" target="_blank" >https://doi.org/10.4230/LIPIcs.ICALP.2022.47</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2022.47" target="_blank" >10.4230/LIPIcs.ICALP.2022.47</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Streaming Algorithms for Geometric Steiner Forest

Popis výsledku v původním jazyce

We consider an important generalization of the Steiner tree problem, the Steiner forest problem, in the Euclidean plane: the input is a multiset X SUBSET OF OR EQUAL TO   ℝ2, partitioned into k color classes C1, C2,..., Ck SUBSET OF OR EQUAL TO   X. The goal is to find a minimum-cost Euclidean graph G such that every color class Ci is connected in G. We study this Steiner forest problem in the streaming setting, where the stream consists of insertions and deletions of points to X. Each input point x ELEMENT OF X arrives with its color color(x) ELEMENT OF [k], and as usual for dynamic geometric streams, the input is restricted to the discrete grid {0,..., INCREMENT }2. We design a single-pass streaming algorithm that uses poly(k . log INCREMENT ) space and time, and estimates the cost of an optimal Steiner forest solution within ratio arbitrarily close to the famous Euclidean Steiner ratio α2 (currently 1.1547 &lt;= α2 &lt;= 1.214). This approximation guarantee matches the state of the art bound for streaming Steiner tree, i.e., when k = 1. Our approach relies on a novel combination of streaming techniques, like sampling and linear sketching, with the classical Arora-style dynamic-programming framework for geometric optimization problems, which usually requires large memory and has so far not been applied in the streaming setting. We complement our streaming algorithm for the Steiner forest problem with simple arguments showing that any finite approximation requires Ω(k) bits of space. (C) Artur Czumaj, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý; licensed under Creative Commons License CC-BY 4.0

Název v anglickém jazyce

Streaming Algorithms for Geometric Steiner Forest

Popis výsledku anglicky

We consider an important generalization of the Steiner tree problem, the Steiner forest problem, in the Euclidean plane: the input is a multiset X SUBSET OF OR EQUAL TO   ℝ2, partitioned into k color classes C1, C2,..., Ck SUBSET OF OR EQUAL TO   X. The goal is to find a minimum-cost Euclidean graph G such that every color class Ci is connected in G. We study this Steiner forest problem in the streaming setting, where the stream consists of insertions and deletions of points to X. Each input point x ELEMENT OF X arrives with its color color(x) ELEMENT OF [k], and as usual for dynamic geometric streams, the input is restricted to the discrete grid {0,..., INCREMENT }2. We design a single-pass streaming algorithm that uses poly(k . log INCREMENT ) space and time, and estimates the cost of an optimal Steiner forest solution within ratio arbitrarily close to the famous Euclidean Steiner ratio α2 (currently 1.1547 &lt;= α2 &lt;= 1.214). This approximation guarantee matches the state of the art bound for streaming Steiner tree, i.e., when k = 1. Our approach relies on a novel combination of streaming techniques, like sampling and linear sketching, with the classical Arora-style dynamic-programming framework for geometric optimization problems, which usually requires large memory and has so far not been applied in the streaming setting. We complement our streaming algorithm for the Steiner forest problem with simple arguments showing that any finite approximation requires Ω(k) bits of space. (C) Artur Czumaj, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý; licensed under Creative Commons License CC-BY 4.0

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

<a href="/cs/project/GX19-27871X" target="_blank" >GX19-27871X: Efektivní aproximační algoritmy a obvodová složitost</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-235-8

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

20

Strana od-do

—

Název nakladatele

Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Místo vydání

Dagstuhl, Germany

Místo konání akce

Paříž, Francie

Datum konání akce

4. 7. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—