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Approximate Representation of Symmetric Submodular Functions via Hypergraph Cut Functions

Authors Calvin Beideman, Karthekeyan Chandrasekaran, Chandra Chekuri, Chao Xu

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Author Details

Calvin Beideman
  • University of Illinois, Urbana-Champaign, IL, USA
Karthekeyan Chandrasekaran
  • University of Illinois, Urbana-Champaign, USA
Chandra Chekuri
  • University of Illinois, Urbana-Champaign, USA
Chao Xu
  • University of Electronic Science and Technology of China, Chengdu, China

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Calvin Beideman, Karthekeyan Chandrasekaran, Chandra Chekuri, and Chao Xu. Approximate Representation of Symmetric Submodular Functions via Hypergraph Cut Functions. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 6:1-6:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Submodular functions are fundamental to combinatorial optimization. Many interesting problems can be formulated as special cases of problems involving submodular functions. In this work, we consider the problem of approximating symmetric submodular functions everywhere using hypergraph cut functions. Devanur, Dughmi, Schwartz, Sharma, and Singh [Devanur et al., 2013] showed that symmetric submodular functions over n-element ground sets cannot be approximated within (n/8)-factor using a graph cut function and raised the question of approximating them using hypergraph cut functions. Our main result is that there exist symmetric submodular functions over n-element ground sets that cannot be approximated within a o(n^{1/3}/log² n)-factor using a hypergraph cut function. On the positive side, we show that symmetrized concave linear functions and symmetrized rank functions of uniform matroids and partition matroids can be constant-approximated using hypergraph cut functions.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Submodular Functions
  • Hypergraphs
  • Approximation
  • Representation


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