One Tree to Rule Them All: Poly-Logarithmic Universal Steiner Tree

Ostas Busch, Da Qi Chen, Arnold Filtser, Daniel Hathcock, D. Ellis Hershkowitz, Rajmohan Rajaraman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A spanning tree T of graph G is a ρ-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a ρ factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2O(√log n)-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions.We settle these open questions by giving polynomial-time algorithms for computing both O(log 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. We reduce the existence of these objects to the previously studied cluster aggregation problem and a class of well-separated point sets which we call dangling nets. For graphs with constant doubling dimension or constant pathwidth we obtain improved bounds by deriving O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms.

Original languageEnglish
Title of host publicationProceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023
PublisherIEEE Computer Society
Pages60-76
Number of pages17
ISBN (Electronic)9798350318944
DOIs
StatePublished - 2023
Event64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023 - Santa Cruz, United States
Duration: 6 Nov 20239 Nov 2023

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023
Country/TerritoryUnited States
CitySanta Cruz
Period6/11/239/11/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Funding

Busch supported by National Science Foundation grant CNS-2131538. Filtser supported by the Israel Science Foundation (grant No. 1042/22). Hathcock supported by the National Science Foundation Graduate Research Fellowship under grant No. DGE-2140739. Hershkowitz funded by the SNSF, Swiss National Science Foundation grant 200021 184622. Rajaraman supported by National Science Foundation grant CCF-1909363.

FundersFunder number
National Science FoundationCNS-2131538
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung200021 184622, CCF-1909363
Israel Science FoundationDGE-2140739, 1042/22

    Keywords

    • Steiner trees
    • approximation algorithms
    • metric embeddings
    • universal algorithms

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