16,549 research outputs found
Combinatorial algorithms for inverse network flow problems
"(Revised January 25, 1998)"--T.p. -- "February 1998."--Cover.Includes bibliographical references (p. 23-25).Supported by a grant from the United Parcel Service and a contract from the Office of Naval Research. ONR N00014-96-1-0051Ravindra K. Ahuja, James B. Orlin
Optimal Topology Design for Disturbance Minimization in Power Grids
The transient response of power grids to external disturbances influences
their stable operation. This paper studies the effect of topology in linear
time-invariant dynamics of different power grids. For a variety of objective
functions, a unified framework based on norm is presented to analyze the
robustness to ambient fluctuations. Such objectives include loss reduction,
weighted consensus of phase angle deviations, oscillations in nodal frequency,
and other graphical metrics. The framework is then used to study the problem of
optimal topology design for robust control goals of different grids. For radial
grids, the problem is shown as equivalent to the hard "optimum communication
spanning tree" problem in graph theory and a combinatorial topology
construction is presented with bounded approximation gap. Extended to loopy
(meshed) grids, a greedy topology design algorithm is discussed. The
performance of the topology design algorithms under multiple control objectives
are presented on both loopy and radial test grids. Overall, this paper analyzes
topology design algorithms on a broad class of control problems in power grid
by exploring their combinatorial and graphical properties.Comment: 6 pages, 3 figures, a version of this work will appear in ACC 201
A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching
We study the quadratic assignment problem, in computer vision also known as
graph matching. Two leading solvers for this problem optimize the Lagrange
decomposition duals with sub-gradient and dual ascent (also known as message
passing) updates. We explore s direction further and propose several additional
Lagrangean relaxations of the graph matching problem along with corresponding
algorithms, which are all based on a common dual ascent framework. Our
extensive empirical evaluation gives several theoretical insights and suggests
a new state-of-the-art any-time solver for the considered problem. Our
improvement over state-of-the-art is particularly visible on a new dataset with
large-scale sparse problem instances containing more than 500 graph nodes each.Comment: Added acknowledgment
Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems
Optimization methods are at the core of many problems in signal/image
processing, computer vision, and machine learning. For a long time, it has been
recognized that looking at the dual of an optimization problem may drastically
simplify its solution. Deriving efficient strategies which jointly brings into
play the primal and the dual problems is however a more recent idea which has
generated many important new contributions in the last years. These novel
developments are grounded on recent advances in convex analysis, discrete
optimization, parallel processing, and non-smooth optimization with emphasis on
sparsity issues. In this paper, we aim at presenting the principles of
primal-dual approaches, while giving an overview of numerical methods which
have been proposed in different contexts. We show the benefits which can be
drawn from primal-dual algorithms both for solving large-scale convex
optimization problems and discrete ones, and we provide various application
examples to illustrate their usefulness
An O(1)-Approximation for Minimum Spanning Tree Interdiction
Network interdiction problems are a natural way to study the sensitivity of a
network optimization problem with respect to the removal of a limited set of
edges or vertices. One of the oldest and best-studied interdiction problems is
minimum spanning tree (MST) interdiction. Here, an undirected multigraph with
nonnegative edge weights and positive interdiction costs on its edges is given,
together with a positive budget B. The goal is to find a subset of edges R,
whose total interdiction cost does not exceed B, such that removing R leads to
a graph where the weight of an MST is as large as possible. Frederickson and
Solis-Oba (SODA 1996) presented an O(log m)-approximation for MST interdiction,
where m is the number of edges. Since then, no further progress has been made
regarding approximations, and the question whether MST interdiction admits an
O(1)-approximation remained open.
We answer this question in the affirmative, by presenting a 14-approximation
that overcomes two main hurdles that hindered further progress so far.
Moreover, based on a well-known 2-approximation for the metric traveling
salesman problem (TSP), we show that our O(1)-approximation for MST
interdiction implies an O(1)-approximation for a natural interdiction version
of metric TSP
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