Streaming Algorithms for Geometric Steiner Forest
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493442" target="_blank" >RIV/00216208:11320/24:10493442 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_8m-4DeLtv" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_8m-4DeLtv</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/3663666" target="_blank" >10.1145/3663666</a>
Alternative languages
Result language
angličtina
Original language name
Streaming Algorithms for Geometric Steiner Forest
Original language description
We consider a generalization of the Steiner tree problem, the Steiner forest problem, in the Euclidean plane: the input is a multiset X subset of R2, partitioned into k color classes C1,. .. , C k subset of X . The goal is to find a minimum-cost Euclidean graph G such that every color class C 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 is an element of X arrives with its color color(x) is an element of [k], and as usual for dynamic geometric streams, the input is restricted to the discrete grid {1, ... , Delta }2. We design a single-pass streaming algorithm that uses poly(k <middle dot> log Delta) space and time, and estimates the cost of an optimal Steiner forest solution within ratio arbitrarily close to the famous Euclidean Steiner ratio a 2 (currently 1.1547 <= a 2 <= 1.214). This approximation guarantee matches the state-of-the-art bound for streaming Steiner tree, i.e., when k = 1, and it is a major open question to improve the ratio to 1 + & even for this special case. 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 so far has not been applied in the streaming setting. We complement our streaming algorithm for the Steiner forest problem with simple arguments showing that any finite multiplicative approximation requires Omega (k) bits of space.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ACM Transactions on Algorithms
ISSN
1549-6325
e-ISSN
1549-6333
Volume of the periodical
20
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
38
Pages from-to
28
UT code for WoS article
001356761000007
EID of the result in the Scopus database
2-s2.0-85207020419