Book Review: Submodular functions and optimization theory
نویسندگان
چکیده
منابع مشابه
Submodular Functions: Optimization and Approximation
Submodular functions are discrete analogue of convex functions, arising in various fields of applied mathematics including game theory, information theory, and queueing theory. This survey aims at providing an overview on fundamental properties of submodular functions and recent algorithmic developments of their optimization and approximation. For submodular function minimization, the ellipsoid...
متن کاملSubmodular functions in graph theory
Frank, A., Submodular functions in graph theory, Discrete Mathematics 111 (1993) 231-243. We describe various aspects of the use of submodular functions in graph theory. New proofs of theorems of Mader and of Tutte are provided as well as a new application on making a digraph k-edge-connected by adding a minimum number of edges.
متن کاملSubmodular Functions: Learnability, Structure, and Optimization
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In this work we study submodular functions from a learning theoretic angle. We provide algorithms for learning submodular functions, as well as lower bounds on the...
متن کاملLearning and Optimization with Submodular Functions
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast und...
متن کاملMulti-Agent Combinatorial Optimization under Submodular Functions
Submodular functions are the discrete ananlogue of convexity and generalize many known and well studied settings. They capture several economic principles such as decreasing marginal cost and correlated utilities. Multi-agent allocation problems over submodular functions arise in a variety of natural scenarios and have been the subject of extensive study over the last decade. In this proposal I...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1993
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1993-00387-2