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Approximating submodular functions everywhere
- M. Goemans, Nicholas J. A. Harvey, S. Iwata, V. Mirrokni
- Mathematics, Computer ScienceSODA
- 4 January 2009
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.
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…
Submodular Function Minimization under Covering Constraints
- S. Iwata, K. Nagano
- Mathematics, Computer Science50th Annual IEEE Symposium on Foundations of…
- 25 October 2009
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.
A push-relabel framework for submodular function minimization and applications to parametric optimization
A fully combinatorial algorithm for submodular function minimization
- S. Iwata
- MathematicsSODA '02
- 27 July 2001
This paper presents a strongly polynomial algorithm for submodular function minimization using only additions, subtractions, comparisons, and oracle calls for function values.
Solving the Trust-Region Subproblem By a Generalized Eigenvalue Problem
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.
Submodular function minimization
- S. Iwata
- MathematicsMath. Program.
- 19 July 2007
This survey paper gives overview on the fundamental properties of submodular functions and recent algorithmic devolopments of their minimization.
Minimum Average Cost Clustering
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.
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…
A weighted linear matroid parity algorithm
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.