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.APPROX/RANDOM.2023.23
URN: urn:nbn:de:0030-drops-188484
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18848/
Go to the corresponding LIPIcs Volume Portal

Patton, Kalen ; Russo, Matteo ; Singla, Sahil

Submodular Norms with Applications To Online Facility Location and Stochastic Probing

pdf-format:
LIPIcs-APPROX23.pdf (0.9 MB)

Abstract

Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond ?_p norms. Our work introduces the concept of submodular norms, which are a versatile type of norms that possess marginal properties similar to submodular set functions. We show that submodular norms can either accurately represent or approximate well-known classes of norms, such as ?_p norms, ordered norms, and symmetric norms. Furthermore, we establish that submodular norms can be applied to optimization problems such as online facility location and stochastic probing. This allows us to develop a logarithmic-competitive algorithm for online facility location with symmetric norms, and to prove logarithmic adaptivity gap for stochastic probing with symmetric norms.

BibTeX - Entry

@InProceedings{patton_et_al:LIPIcs.APPROX/RANDOM.2023.23,
  author =	{Patton, Kalen and Russo, Matteo and Singla, Sahil},
  title =	{{Submodular Norms with Applications To Online Facility Location and Stochastic Probing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18848},
  URN =		{urn:nbn:de:0030-drops-188484},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.23},
  annote =	{Keywords: Submodularity, Monotone Norms, Online Facility Location, Stochastic Probing}
}

Keywords: Submodularity, Monotone Norms, Online Facility Location, Stochastic Probing
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)
Issue Date: 2023
Date of publication: 04.09.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI