@inproceedings{a9449e9e22904a3896f92ec43959c372,

title = "One Tree to Rule Them All: Poly-Logarithmic Universal Steiner Tree",

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.",

keywords = "approximation algorithms, metric embeddings, Steiner trees, universal algorithms",

author = "Ostas Busch and Chen, {Da Qi} and Arnold Filtser and Daniel Hathcock and Hershkowitz, {D. Ellis} and Rajmohan Rajaraman",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023 ; Conference date: 06-11-2023 Through 09-11-2023",

year = "2023",

month = jan,

day = "1",

doi = "10.1109/FOCS57990.2023.00012",

language = "English",

series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",

publisher = "Institute of Electrical and Electronics Engineers",

pages = "60--76",

booktitle = "Proceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023",

address = "United States",

}