License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2023.83
URN: urn:nbn:de:0030-drops-175863
URL: https://drops.dagstuhl.de/opus/volltexte/2023/17586/
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Liu, Yang P.

Vertex Sparsification for Edge Connectivity in Polynomial Time

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LIPIcs-ITCS-2023-83.pdf (0.7 MB)


Abstract

An important open question in the area of vertex sparsification is whether (1+ε)-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist. The work [Parinya Chalermsook et al., 2021] (SODA 2021) introduced a relaxation called connectivity-c mimicking networks, which asks to construct a vertex sparsifier which preserves connectivity among k terminals exactly up to the value of c, and showed applications to dynamic connectivity data structures and survivable network design. We show that connectivity-c mimicking networks with Õ(kc³) edges exist and can be constructed in polynomial time in n and c, improving over the results of [Parinya Chalermsook et al., 2021] for any c ≥ log n, whose runtimes depended exponentially on c.

BibTeX - Entry

@InProceedings{liu:LIPIcs.ITCS.2023.83,
  author =	{Liu, Yang P.},
  title =	{{Vertex Sparsification for Edge Connectivity in Polynomial Time}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{83:1--83:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17586},
  URN =		{urn:nbn:de:0030-drops-175863},
  doi =		{10.4230/LIPIcs.ITCS.2023.83},
  annote =	{Keywords: Vertex-sparsification, edge-connectivity, Gammoids}
}

Keywords: Vertex-sparsification, edge-connectivity, Gammoids
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023


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