Book Chapter10.1016/S0927-0507(05)12007-6
Submodular Function Minimization
S. Thomas McCormick
- 01 Jan 2005
- Vol. 12, pp 321-391
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.
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Abstract: 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, by Iwata, Fleischer and Fujishige, and by Iwata for solving it; and extensions of SFM to more general families of subsets.
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Citations
•Book
Submodular functions and optimization
悟 藤重
- 01 Jan 1991
TL;DR: In this paper, the Lovasz Extensions of Submodular Functions are extended to include nonlinear weight functions and linear weight functions with continuous variables, and a Decomposition Algorithm is proposed.
823
A faster strongly polynomial time algorithm for submodular function minimization
TL;DR: A combinatorial algorithm that runs in O(n5EO + n6) time, where EO is the time to evaluate f(S) for some submodular function f defined on a set V with n elements is given.
373
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).
355
Submodular function minimization
TL;DR: This survey paper gives overview on the fundamental properties of submodular functions and recent algorithmic devolopments of their minimization.
Appointment Scheduling with Discrete Random Durations
TL;DR: This model can handle a given due date for the total processing of a given sequence of jobs after which overtime is incurred and, no-shows and emergencies.
161
References
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Computers and Intractability: A Guide to the Theory of NP-Completeness
Michael Randolph Garey,David S. Johnson +1 more
- 01 Jan 1979
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
•Book
Network Flows: Theory, Algorithms, and Applications
Ravindra K. Ahuja,Thomas L. Magnanti,James B. Orlin +2 more
- 01 Jan 1993
TL;DR: In-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models are presented.
•Book
Nonnegative Matrices in the Mathematical Sciences
Abraham Berman
- 01 Aug 1979
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
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•Book
Integer and Combinatorial Optimization
George L. Nemhauser,Laurence A. Wolsey +1 more
- 01 Jan 1988
TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
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