1 Search Results for "Ramaswamy, Vidhya"

Document
DOI: 10.4230/LIPIcs.ITCS.2020.64
New Query Lower Bounds for Submodular Function Minimization

Authors: Andrei Graur, Tristan Pollner, Vidhya Ramaswamy, and S. Matthew Weinberg

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
We consider submodular function minimization in the oracle model: given black-box access to a submodular set function f:2^[n] → ℝ, find an element of arg min_S {f(S)} using as few queries to f(⋅) as possible. State-of-the-art algorithms succeed with Õ(n²) queries [Yin Tat Lee et al., 2015], yet the best-known lower bound has never been improved beyond n [Nicholas J. A. Harvey, 2008]. We provide a query lower bound of 2n for submodular function minimization, a 3n/2-2 query lower bound for the non-trivial minimizer of a symmetric submodular function, and a binom{n}{2} query lower bound for the non-trivial minimizer of an asymmetric submodular function. Our 3n/2-2 lower bound results from a connection between SFM lower bounds and a novel concept we term the cut dimension of a graph. Interestingly, this yields a 3n/2-2 cut-query lower bound for finding the global mincut in an undirected, weighted graph, but we also prove it cannot yield a lower bound better than n+1 for s-t mincut, even in a directed, weighted graph.
Cite as

Andrei Graur, Tristan Pollner, Vidhya Ramaswamy, and S. Matthew Weinberg. New Query Lower Bounds for Submodular Function Minimization. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{graur_et_al:LIPIcs.ITCS.2020.64,
  author =	{Graur, Andrei and Pollner, Tristan and Ramaswamy, Vidhya and Weinberg, S. Matthew},
  title =	{{New Query Lower Bounds for Submodular Function Minimization}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.64},
  URN =		{urn:nbn:de:0030-drops-117493},
  doi =		{10.4230/LIPIcs.ITCS.2020.64},
  annote =	{Keywords: submodular functions, query lower bounds, min cut}
}
  • Refine by Author
  • 1 Graur, Andrei
  • 1 Pollner, Tristan
  • 1 Ramaswamy, Vidhya
  • 1 Weinberg, S. Matthew

  • Refine by Classification
  • 1 Theory of computation → Submodular optimization and polymatroids

  • Refine by Keyword
  • 1 min cut
  • 1 query lower bounds
  • 1 submodular functions

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2020

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact