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Approximating submodular functions everywhere
TLDR
The problem of approximating a non-negative, monotone, submodular function f on a ground set of size n everywhere is considered, after only poly(n) oracle queries, and it is shown that no algorithm can achieve a factor better than Ω(√n/log n), even for rank functions of a matroid.
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A combinatorial strongly polynomial algorithm for minimizing submodular functions
This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grötschel, Lovász, and Schrijver. The algorithm employs…
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Submodular Function Minimization under Covering Constraints
  • S. Iwata, K. Nagano
  • Mathematics, Computer Science
    50th Annual IEEE Symposium on Foundations of…
  • 25 October 2009
TLDR
This paper presents a rounding 2-approximation algorithm for the sub modular vertex cover problem based on the half-integrality of the continuous relaxation problem, and shows that the rounding algorithm can be performed by one application of submodular function minimization on a ring family.
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A push-relabel framework for submodular function minimization and applications to parametric optimization
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A fully combinatorial algorithm for submodular function minimization
This paper presents a strongly polynomial algorithm for submodular function minimization using only additions, subtractions, comparisons, and oracle calls for function values.
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Solving the Trust-Region Subproblem By a Generalized Eigenvalue Problem
TLDR
It is demonstrated that the resulting algorithm is a general-purpose TRS solver, effective both for dense and large-sparse problems, including the so-called hard case, and obtaining approximate solutions efficiently when high accuracy is unnecessary.
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Submodular function minimization
  • S. Iwata
  • Mathematics
    Math. Program.
  • 19 July 2007
TLDR
This survey paper gives overview on the fundamental properties of submodular functions and recent algorithmic devolopments of their minimization.
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Minimum Average Cost Clustering
TLDR
The minimum average cost clustering problem is parameterized with a real variable, and surprisingly, it is shown that all information about optimal clusterings for all parameters can be computed in polynomial time in total.
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A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions
This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grotschel, Lov asz, and Schrijver. The algorithm employs…
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A weighted linear matroid parity algorithm
TLDR
This paper presents a combinatorial, deterministic, strongly polynomial algorithm for the weighted linear matroid parity problem and adopts a primal-dual approach with the aid of the augmenting path algorithm of Gabow and Stallmann (1986) for the unweighted problem.
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