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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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fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 423 (37 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity
Exponentially Dense Matroids
, 2011
"... This thesis deals with questions relating to the maximum density of rankn matroids in a minorclosed class. Consider a minorclosed class M of matroids that does not contain a given rank2 uniform matroid. The growth rate function is defined by hM(n) = max (M  : M ∈M simple, r(M) ≤ n). The Gro ..."
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Cited by 5 (5 self)
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This thesis deals with questions relating to the maximum density of rankn matroids in a minorclosed class. Consider a minorclosed class M of matroids that does not contain a given rank2 uniform matroid. The growth rate function is defined by hM(n) = max (M  : M ∈M simple, r(M) ≤ n
Evolutionary algorithms and matroid optimization problems
"... We analyze the performance of evolutionary algorithms on various matroid optimization problems that encompass a vast number of efficiently solvable as well as NPhard combinatorial optimization problems (including many wellknown examples such as minimum spanning tree and maximum bipartite matching ..."
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Cited by 11 (2 self)
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We analyze the performance of evolutionary algorithms on various matroid optimization problems that encompass a vast number of efficiently solvable as well as NPhard combinatorial optimization problems (including many wellknown examples such as minimum spanning tree and maximum bipartite
CONVEX MATROID OPTIMIZATION
, 2003
"... We consider a problem of maximizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally intractable, we show that it is efficiently solvable when a suitable parameter is restricted. ..."
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Cited by 8 (5 self)
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We consider a problem of maximizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally intractable, we show that it is efficiently solvable when a suitable parameter is restricted.
The Matroid Median Problem
"... In the classical kmedian problem, we are given a metric space and would like to openk centers so as to minimize the sum (over all the vertices) of the distance of each vertex to its nearest open center. In this paper, we consider the following generalization of the problem: instead of opening at mo ..."
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Cited by 10 (2 self)
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In the classical kmedian problem, we are given a metric space and would like to openk centers so as to minimize the sum (over all the vertices) of the distance of each vertex to its nearest open center. In this paper, we consider the following generalization of the problem: instead of opening
Computation in Multicriteria Matroid Optimization
"... Motivated by recent work on algorithmic theory for nonlinear and multicriteria matroid optimization, we have developed algorithms and heuristics aimed at practical solution of large instances of some of these difficult problems. Our methods primarily use the local adjacency structure inherent in mat ..."
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Cited by 2 (1 self)
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Motivated by recent work on algorithmic theory for nonlinear and multicriteria matroid optimization, we have developed algorithms and heuristics aimed at practical solution of large instances of some of these difficult problems. Our methods primarily use the local adjacency structure inherent
A formal analysis and taxonomy of task allocation in multirobot systems
 INT’L. J. OF ROBOTICS RESEARCH
, 2004
"... Despite more than a decade of experimental work in multirobot systems, important theoretical aspects of multirobot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multirobot task allocation (MRTA). Most work on MRTA has been ad hoc ..."
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Cited by 297 (4 self)
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problems is given, and it is shown how many such problems can be viewed as instances of other, wellstudied, optimization problems. We demonstrate how relevant theory from operations research and combinatorial optimization can be used for analysis and greater understanding of existing approaches to task
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