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371
Divideandconquer algorithms for partitioning hypergraphs and submodular systems
, 2009
"... The submodular system kpartition problem is a problem of partitioning a given finite set V into k nonempty subsets V1, V2,..., Vk so that P k i=1 f(Vi) is minimized where f is a nonnegative submodular function on V, and k is a fixed integer. This problem contains the hypergraph kcut problem. In ..."
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Cited by 4 (1 self)
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The submodular system kpartition problem is a problem of partitioning a given finite set V into k nonempty subsets V1, V2,..., Vk so that P k i=1 f(Vi) is minimized where f is a nonnegative submodular function on V, and k is a fixed integer. This problem contains the hypergraph kcut problem
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can
Approximation algorithms for submodular multiway partition
 CoRR
"... Abstract — We study algorithms for the SUBMODULAR MUL ..."
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Cited by 9 (2 self)
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Abstract — We study algorithms for the SUBMODULAR MUL
Submodular Approximation: Samplingbased Algorithms and Lower Bounds
, 2008
"... We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load balancing or minimummakespan scheduling, submodular sparsest cu ..."
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Cited by 38 (0 self)
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value oracle. The approximation guarantees for most of our algorithms are of the order of √ n/lnn. We show that this is the inherent difficulty of the problems by proving matching lower bounds. We also give an improved lower bound for the problem of approximately learning a monotone submodular function
Active Learning and Submodular Functions
, 2012
"... Active learning is a machine learning setting where the learning algorithm decides what data is labeled. Submodular functions are a class of set functions for which many optimization problems have efficient exact or approximate algorithms. We examine their connections. • We propose a new class of in ..."
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Active learning is a machine learning setting where the learning algorithm decides what data is labeled. Submodular functions are a class of set functions for which many optimization problems have efficient exact or approximate algorithms. We examine their connections. • We propose a new class
APPROXIMATION ALGORITHMS FOR SUBMODULAR OPTIMIZATION AND GRAPH PROBLEMS
, 2013
"... In this thesis, we consider combinatorial optimization problems involving submodular functions and graphs. The problems we study are NPhard and therefore, assuming that P 6 = NP, there do not exist polynomialtime algorithms that always output an optimal solution. In order to cope with the intracta ..."
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In this thesis, we consider combinatorial optimization problems involving submodular functions and graphs. The problems we study are NPhard and therefore, assuming that P 6 = NP, there do not exist polynomialtime algorithms that always output an optimal solution. In order to cope
Submodular cost allocation problem and applications
 Proc. of ICALP, 354–366
, 2011
"... Abstract. We study the Minimum SubmodularCost Allocation problem (MSCA). In this problem we are given a finite ground set V and k nonnegative submodular set functions f1,..., fk on V. The objective is to partition V into k (possibly empty) sets A1, · · · , Ak such that the sum ∑k i=1 fi(Ai) i ..."
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Cited by 5 (3 self)
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extension for submodular functions. This allows us to understand several previous relaxations and rounding procedures in a unified fashion and also develop new formulations and approximation algorithms for related problems. In particular, we give a (1.5 − 1/k)approximation for the hypergraph multiway partition
Submodular Maximization by Simulated Annealing
"... We consider the problem of maximizing a nonnegative (possibly nonmonotone) submodular set function with or without constraints. Feige et al. [9] showed a 2/5approximation for the unconstrained problem and also proved that no approximation better than 1/2 is possible in the value oracle model. Cons ..."
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Cited by 19 (2 self)
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/4approximation assuming that ν ≥ 2 [33]). In this paper, we propose a new algorithm for submodular maximization which is based on the idea of simulated annealing. We prove that this algorithm achieves improved approximation for two problems: a 0.41approximation for unconstrained submodular maximization, and a 0
Results 1  10
of
371