Corpus ID: 232134951

Decomposable Submodular Function Minimization via Maximum Flow

  title={Decomposable Submodular Function Minimization via Maximum Flow},
  author={Kyriakos Axiotis and Adam Karczmarz and A. Mukherjee and P. Sankowski and Adrian Vladu},
This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a number of calls to a maximum flow oracle. When each function in the decomposition acts on O(1) elements of the ground set V and is polynomially bounded, our running time is up to polylogarithmic factors equal to that of solving maximum flow in a sparse graph with… Expand
1 Citations
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Minimizing a sum of submodular functions
  • V. Kolmogorov
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 2012
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A push-relabel framework for submodular function minimization and applications to parametric optimization
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On the Approximation of Submodular Functions
A large number of prior works imply that monotone submodular functions can be approximated by coverage functions with a factor between $O(\sqrt{n} \log n)$ and $\Omega(n^{1/3} /\log^2 n) $ and this work proves both upper and lower bounds on such approximations. Expand
A combinatorial strongly polynomial algorithm for minimizing submodular functions
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Subquadratic submodular function minimization
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