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Submodular Norms with Applications To Online Facility Location and Stochastic Probing

Authors Kalen Patton, Matteo Russo, Sahil Singla

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Author Details

Kalen Patton
  • School of Mathematics, Georgia Tech, Atlanta, GA, USA
Matteo Russo
  • DIAG, Sapienza Università di Roma, Italy
Sahil Singla
  • School of Computer Science, Georgia Tech, Atlanta, GA, USA

Funding

  • Russo, Matteo: Supported by the ERC Advanced Grant 788893 AMDROMA.

Acknowledgements

We thank the anonymous reviewers of APPROX/RANDOM 2023 for their valuable feedback.

Cite AsGet BibTex

Kalen Patton, Matteo Russo, and Sahil Singla. Submodular Norms with Applications To Online Facility Location and Stochastic Probing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.23

Abstract

Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond 𝓁_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 𝓁_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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • Submodularity
  • Monotone Norms
  • Online Facility Location
  • Stochastic Probing

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