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A Fully Combinatorial Algorithm for Submodular Function Minimization
2002
Journal of combinatorial theory. Series B (Print)
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This paper presents a strongly polynomial algorithm for submodular function minimization using only additions, subtractions, comparisons, and oracle calls for function values. ...
ACKNOWLEDGMENTS The author is very grateful to Yves Crama, Satoru Fujishige, Makoto Matsumoto, and Tom McCormick for their helpful comments. ...
A FULLY COMBINATORIAL ALGORITHM This section presents an outline of our fully combinatorial algorithm for minimizing a submodular function f: 2 U Q R. The algorithm consists of iterations. ...
doi:10.1006/jctb.2001.2072
fatcat:vpf5xqngn5dedbz6kdpzjuqtie
A strongly polynomial algorithm for line search in submodular polyhedra
2007
Discrete Optimization
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This paper presents a strongly polynomial time algorithm for line search in submodular polyhedra with the aid of a fully combinatorial algorithm for submodular function minimization as a subroutine. ...
A submodular polyhedron is a polyhedron associated with a submodular function. ...
Acknowledgments I am grateful to Satoru Iwata for a number of useful comments. ...
doi:10.1016/j.disopt.2007.09.002
fatcat:iamsxlekmfbidhv6et7uekaigu
Submodular Functions: Optimization and Approximation
2011
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)
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For submodular function minimization, the ellipsoid method had long been the only polynomial algorithm until combinatorial strongly polynomial algorithms appeared a decade ago. ...
In addition, an efficient method has been developed for approximating submoduar functions everywhere, which leads to a generic framework of designing approximation algorithms for combinatorial optimization ...
As a generalization of this minimum cut algorithm, Queyranne [69] presented a fully combinatorial strongly polynomial algorithm for symmetric submodular function minimization. ...
doi:10.1142/9789814324359_0173
fatcat:uspd2ma2uzco3kvzqiytgxz45a
A Simple Combinatorial Algorithm for Submodular Function Minimization
[chapter]
2009
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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This paper presents a new simple algorithm for minimizing submodular functions. ...
This is the first fully combinatorial submodular function minimization algorithm that does not rely on the scaling method. ...
Acknowledgements The authors are grateful to Tom McCormick for helpful comments on the manuscript. The first author thanks the Asahi Glass Foundation for supporting this work. ...
doi:10.1137/1.9781611973068.133
fatcat:kkaihia2m5f7piylc6r4unzgiy
Submodular function minimization
2007
Mathematical programming
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In this survey paper, we give overview on the fundamental properties of submodular functions and recent algorithmic devolopments of their minimization. ...
Submodular functions often arise in various fields of operations research including discrete optimization, game theory, queueing theory and information theory. ...
Acknowledgements The author thanks Fabian Chudak, Lisa Fleischer, Satoru Fujishige, and Tom McCormick for fruitful discussions on the topics of this paper. ...
doi:10.1007/s10107-006-0084-2
fatcat:sjlv5itvhrfanb2ncjpsapvyn4
A Faster Scaling Algorithm for Minimizing Submodular Functions
[chapter]
2002
Lecture Notes in Computer Science
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This paper combines the scaling scheme with the push/relabel framework to yield a faster combinatorial algorithm for submodular function minimization. ...
Combinatorial strongly polynomial algorithms for minimizing submodular functions have been developed by Iwata, Fleischer, and Fujishige (IFF) and by Schrijver. ...
fully combinatorial version. ...
doi:10.1007/3-540-47867-1_1
fatcat:zt33bi5g5jb7jneznrdl2qcote
A Faster Scaling Algorithm for Minimizing Submodular Functions
2003
SIAM journal on computing (Print)
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This paper combines the scaling scheme with the push/relabel framework to yield a faster combinatorial algorithm for submodular function minimization. ...
Combinatorial strongly polynomial algorithms for minimizing submodular functions have been developed by Iwata, Fleischer, and Fujishige (IFF) and by Schrijver. ...
fully combinatorial version. ...
doi:10.1137/s0097539701397813
fatcat:rbge2fnm4rb2rfuxocdtqu66fm
Page 5846 of Mathematical Reviews Vol. , Issue 2004g
[page]
2004
Mathematical Reviews
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Summary: “It had been a long-standing open problem to devise a combinatorial polynomial algorithm for minimizing submodular functions. ...
Also, an algorithm for minimizing a submodular function on a distributive lattice is briefly described. ...
A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time
2000
Journal of combinatorial theory. Series B (Print)
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We give a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle. The algorithm does not use the ellipsoid method or any other linear programming method. ...
No bound on the complexity of the values of f is needed to be known a priori. The number of oracle calls is bounded by a polynomial in the size of the underlying set. ...
One would wish to have a "fully combinatorial" algorithm, in which the function values are only compared, added, and subtracted. ...
doi:10.1006/jctb.2000.1989
fatcat:j3burxxwevdodfyxjoqnx34esu
Distributed Submodular Minimization over Networks: a Greedy Column Generation Approach
[article]
2018
arXiv
pre-print
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The challenge is that the (submodular) objective set-function is only partially known by agents, that is, each one is able to evaluate the function only for subsets including itself. ...
In this paper, we consider agents in an asynchronous, unreliable and time-varying directed network that aim at cooperatively solving submodular minimization problems in a fully distributed way. ...
In [21] , a fully distributed algorithm is proposed to minimize the sum of local submodular functions over lattices and applied to motion coordination. ...
arXiv:1812.05974v1
fatcat:u7cuwffrwjeehfeefivadzws5u
Distributed Submodular Minimization Over Networks: A Greedy Column Generation Approach
2018
2018 IEEE Conference on Decision and Control (CDC)
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The challenge is that the (submodular) objective set-function is only partially known by agents, that is, each one is able to evaluate the function only for subsets including itself. ...
In this paper, we consider agents in an asynchronous, unreliable and time-varying directed network that aim at cooperatively solving submodular minimization problems in a fully distributed way. ...
In [21] , a fully distributed algorithm is proposed to minimize the sum of local submodular functions over lattices and applied to motion coordination. ...
doi:10.1109/cdc.2018.8618958
dblp:conf/cdc/TestaNN18
fatcat:sr7thfooavhrdgrujsgzrzsrt4
A combinatorial strongly polynomial algorithm for minimizing submodular functions
2001
Journal of the ACM
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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 resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value. ...
We are grateful to Bill Cunningham, Michel Goemans, and Maiko Shigeno for their useful comments. ...
doi:10.1145/502090.502096
fatcat:omcg327kcjgspl5ge6xzaujpje
Personal reminiscence: combinatorial and discrete optimization problems in which I have been interested
2012
Japan journal of industrial and applied mathematics
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The present article takes up some of the author's research activities in the field of combinatorial and discrete optimization from 1975 till quite recently. ...
They are written together with personal reminiscence and with the hope that this article will convey to researchers of younger generation the author's enthusiasm in combinatorial and discrete optimization ...
This had long kept motivating me to try to devise an efficient algorithm for submodular function minimization. ...
doi:10.1007/s13160-012-0085-x
fatcat:4cpw3vze4rgp7isrea6c5eemqe
Robust Submodular Minimization with Applications to Cooperative Modeling
[article]
2020
arXiv
pre-print
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This paper studies the problem of robust submodular minimization subject to combinatorial constraints. ...
While several existing papers have studied robust submodular maximization, ours is the first work to study the minimization version under a broad range of combinatorial constraints including cardinality ...
Majorization-Minimization Algorithm The Majorization-Minimization algorithm is a sequential procedure which uses upper bounds of the submodular functions defined via supergradients. ...
arXiv:2001.09360v1
fatcat:og7rzbr7zvazji6pd342nd3zdu
Combinatorial optimization for low bit-width neural networks
[article]
2022
arXiv
pre-print
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In this paper, we explore methods of direct combinatorial optimization in the problem of risk minimization with binary weights, which can be made equivalent to a non-monotone submodular maximization under ...
We employ an approximation algorithm for the cases with single and multilayer neural networks. For linear models, it has 𝒪(nd) time complexity where n is the sample size and d is the data dimension. ...
Submodularity and Convexity Submodular functions play an important role in combinatorial optimization when minimizing (or maximizing) a set function defined on the power set P(V ), similar to convex functions ...
arXiv:2206.02006v1
fatcat:tpgip7umqnfbjeetvis47wb5pe
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