A simple combinatorial algorithm for submodular function minimization
Satoru Iwata,James B. Orlin +1 more
- 06 Jan 2002
- pp 915-919
TL;DR: For integer valued submodular functions, the algorithm in this article runs in O(n6EO log nM) time, where n is the cardinality of the ground set, M is the maximum absolute value of the function value, and EO is the time for function evaluation.
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Abstract: This paper presents a new simple algorithm for minimizing submodular functions. For integer valued submodular functions, the algorithm runs in O(n6EO log nM) time, where n is the cardinality of the ground set, M is the maximum absolute value of the function value, and EO is the time for function evaluation. The algorithm can be improved to run in O ((n4EO+n5)log nM) time. The strongly polynomial version of this faster algorithm runs in O((n5EO + n6) log n) time for real valued general submodular functions. These are comparable to the best known running time bounds for submodular function minimization. The algorithm can also be implemented in strongly polynomial time using only additions, subtractions, comparisons, and the oracle calls for function evaluation. This is the first fully combinatorial submodular function minimization algorithm that does not rely on the scaling method.
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Citations
A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization
Yin Tat Lee,Aaron Sidford,Sam Chiu-wai Wong +2 more
- 17 Oct 2015
TL;DR: In this article, the authors improved the running time for finding a point in a convex set given a separation oracle to O(n3 logO(1) nR=a#x03B5).
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Approximating submodular functions everywhere
Michel X. Goemans,Nicholas J. A. Harvey,Satoru Iwata,Vahab Mirrokni +3 more
- 04 Jan 2009
TL;DR: In this article, the problem of finding a monotone, submodular function f on a ground set of size n, after only poly(n) oracle queries was considered.
•Posted Content
Submodular approximation: sampling-based algorithms and lower bounds
Zoya Svitkina,Lisa Fleischer +1 more
TL;DR: In this paper, the authors introduced several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions, and established upper and lower bounds for the approximability of these problems with a polynomial number of queries to a function-value oracle.
155
•Journal Article
Approximating Submodular Functions Everywhere
TL;DR: 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.
151
Submodular Function Minimization
S. Thomas McCormick
- 01 Jan 2005
TL;DR: This chapter describes the submodular function minimization problem (SFM); why it is important; techniques for solving it; algorithms by Cunningham, by Schrijver as modified by Fleischer and Iwata; and extensions of SFM to more general families of subsets.
References
•Book
Geometric Algorithms and Combinatorial Optimization
Martin Grötschel,László Lovász,Alexander Schrijver +2 more
- 01 Jan 1988
TL;DR: In this article, the Fulkerson Prize was won by the Mathematical Programming Society and the American Mathematical Society for proving polynomial time solvability of problems in convexity theory, geometry, and combinatorial optimization.
3.9K
The ellipsoid method and its consequences in combinatorial optimization
TL;DR: The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function.
Cores of Convex Games
TL;DR: In this article, it was shown that the core of a convex game is not empty and that it has an especially regular structure, and that certain other cooperative solution concepts are related in a simple way to the core.
•Book
Submodular functions and optimization
Satoru Fujishige
- 01 Jan 1991
TL;DR: A stacking store having overflow indication and of use for the transmission of binary data in the chronological order of their input (write-in).
1.4K
Submodular functions and convexity
László Lovász
- 01 Jan 1983
TL;DR: In continuous optimization, convex functions play a central role as mentioned in this paper, and various methods for finding the minimum of a convex function constitute the main body of nonlinear optimization, which can be viewed as the optimization of very special (linear) objective functions over very special convex domains (polyhedra).
1.1K
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