On Constructing Spanners from Random Gaussian Projections

Sepehr Assadi, Michael Kapralov, Huacheng Yu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Graph sketching is a powerful paradigm for analyzing graph structure via linear measurements introduced by Ahn, Guha, and McGregor (SODA’12) that has since found numerous applications in streaming, distributed computing, and massively parallel algorithms, among others. Graph sketching has proven to be quite successful for various problems such as connectivity, minimum spanning trees, edge or vertex connectivity, and cut or spectral sparsifiers. Yet, the problem of approximating shortest path metric of a graph, and specifically computing a spanner, is notably missing from the list of successes. This has turned the status of this fundamental problem into one of the most longstanding open questions in this area. We present a partial explanation of this lack of success by proving a strong lower bound for a large family of graph sketching algorithms that encompasses prior work on spanners and many (but importantly not also all) related cut-based problems mentioned above. Our lower bound matches the algorithmic bounds of the recent result of Filtser, Kapralov, and Nouri (SODA’21), up to lower order terms, for constructing spanners via the same graph sketching family. This establishes near-optimality of these bounds, at least restricted to this family of graph sketching techniques, and makes progress on a conjecture posed in this latter work.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2023
EditorsNicole Megow, Adam Smith
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772969
DOIs
StatePublished - Sep 2023
Event26th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2023 and the 27th International Conference on Randomization and Computation, RANDOM 2023 - Atlanta, United States
Duration: Sep 11 2023Sep 13 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume275
ISSN (Print)1868-8969

Conference

Conference26th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2023 and the 27th International Conference on Randomization and Computation, RANDOM 2023
Country/TerritoryUnited States
CityAtlanta
Period9/11/239/13/23

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • graph spanner
  • lower bound
  • sketching algorithm

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