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73
Very LargeScale Neighborhood Search for the Quadratic Assignment Problem
 DISCRETE APPLIED MATHEMATICS
, 2002
"... The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NPhard, and can be solved to optimality only for fairly small size instances ..."
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Cited by 108 (11 self)
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The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NPhard, and can be solved to optimality only for fairly small size instances (typically, n < 25). Neighborhood search algorithms are the most popular heuristic algorithms to solve larger size instances of the QAP. The most extensively used neighborhood structure for the QAP is the 2exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities and thus has size O(n²). Previous efforts to explore larger size neighborhoods (such as 3exchange or 4exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very largescale neighborhood (VLSN) search algorithms where the size of the neighborhood is very large and we propose a novel search procedure to heuristically enumerate good neighbors. Our search procedure relies on the concept of improvement graph which allows us to evaluate neighbors much faster than the existing methods. We present extensive computational results of our algorithms on standard benchmark instances. These investigations reveal that very largescale neighborhood search algorithms give consistently better solutions compared the popular 2exchange neighborhood algorithms considering both the solution time and solution accuracy.
Approximate Join Processing Over Data Streams
, 2003
"... We consider the problem of approximating sliding window joins over data streams in a data stream processing system with limited resources. In our model, we deal with resource constraints by shedding load in the form of dropping tuples from the data streams. We first discuss alternate architectural m ..."
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Cited by 97 (2 self)
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We consider the problem of approximating sliding window joins over data streams in a data stream processing system with limited resources. In our model, we deal with resource constraints by shedding load in the form of dropping tuples from the data streams. We first discuss alternate architectural models for data stream join processing, and we survey suitable measures for the quality of an approximation of a setvalued query result. We then consider the number of generated result tuples as the quality measure, and we give optimal offline and fast online algorithms for it. In a thorough experimental study with synthetic and real data we show the efficacy of our solutions. For applications with demand for exact results we introduce a new Archivemetric which captures the amount of work needed to complete the join in case the streams are archived for later processing.
Algorithms in Discrete Convex Analysis
 Math. Programming
, 2000
"... this paper is to describe the f#eA damental results on M and Lconvex f#24L2A+ with special emphasis on algorithmic aspects. ..."
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Cited by 96 (21 self)
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this paper is to describe the f#eA damental results on M and Lconvex f#24L2A+ with special emphasis on algorithmic aspects.
LAGRANGE MULTIPLIERS AND OPTIMALITY
, 1993
"... Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write firstorder optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions ..."
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Cited by 89 (7 self)
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Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write firstorder optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper understanding of the concept and how it fits into a larger theoretical picture. A major line of research has been the nonsmooth geometry of onesided tangent and normal vectors to the set of points satisfying the given constraints. Another has been the gametheoretic role of multiplier vectors as solutions to a dual problem. Interpretations as generalized derivatives of the optimal value with respect to problem parameters have also been explored. Lagrange multipliers are now being seen as arising from a general rule for the subdifferentiation of a nonsmooth objective function which allows blackandwhite constraints to be replaced by penalty expressions. This paper traces such themes in the current theory of Lagrange multipliers, providing along the way a freestanding exposition of basic nonsmooth analysis as motivated by and applied to this subject.
Framework for Performance Evaluation of Face, Text, and Vehicle Detection and Tracking
 in Video: Data, Metrics, and Protocol”, to appear in IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008. 4. Conclusion In this paper, an
"... Abstract—Common benchmark data sets, standardized performance metrics, and baseline algorithms have demonstrated considerable impact on research and development in a variety of application domains. These resources provide both consumers and developers of technology with a common framework to objecti ..."
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Cited by 31 (3 self)
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Abstract—Common benchmark data sets, standardized performance metrics, and baseline algorithms have demonstrated considerable impact on research and development in a variety of application domains. These resources provide both consumers and developers of technology with a common framework to objectively compare the performance of different algorithms and algorithmic improvements. In this paper, we present such a framework for evaluating object detection and tracking in video: specifically for face, text, and vehicle objects. This framework includes the source video data, groundtruth annotations (along with guidelines for annotation), performance metrics, evaluation protocols, and tools including scoring software and baseline algorithms. For each detection and tracking task and supported domain, we developed a 50clip training set and a 50clip test set. Each data clip is approximately 2.5 minutes long and has been completely spatially/temporally annotated at the Iframe level. Each task/domain, therefore, has an associated annotated corpus of approximately 450,000 frames. The scope of such annotation is unprecedented and was designed to begin to support the necessary quantities of data for robust machine learning approaches, as well as a statistically significant comparison of the performance of algorithms. The goal of this work was to systematically address the challenges of object detection and tracking through a common evaluation framework that permits a meaningful objective comparison of techniques, provides the research community with sufficient data for the exploration of automatic modeling techniques, encourages the incorporation of objective evaluation into the development process, and contributes useful lasting resources of a scale and magnitude that will prove to be extremely useful to the computer vision research community for years to come.
Discrete Optimization in Public Rail Transport
 Math. Programming
, 1997
"... this paper occur at the tactical level. Strategic planning focuses on resource acquisition for the period from five to fifteen years ahead. Network planning problems may be viewed as the main strategic issues, but, in order to evaluate possible strategic alternatives, the subsequent stages including ..."
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Cited by 29 (6 self)
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this paper occur at the tactical level. Strategic planning focuses on resource acquisition for the period from five to fifteen years ahead. Network planning problems may be viewed as the main strategic issues, but, in order to evaluate possible strategic alternatives, the subsequent stages including at least line planning and train schedule generation have to be considered. The disadvantages of the hierarchical planning are obvious, since the optimal output of a subtask which serves as the input of a subsequent task, will not result, in general, in an overall optimal solution.
Solving The Convex Cost Integer Dual Network Flow Problem
 MANAGEMENT SCIENCE
, 1999
"... In this paper, we consider an integer convex optimization problem where the objective function is the sum of separable convex functions (that is, of the form (i,j)Q ij ij F(w)+ iP ii B( ) ), the constraints are similar to those arising in the dual of a minimum cost flow problem (that is, of the f ..."
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Cited by 29 (5 self)
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In this paper, we consider an integer convex optimization problem where the objective function is the sum of separable convex functions (that is, of the form (i,j)Q ij ij F(w)+ iP ii B( ) ), the constraints are similar to those arising in the dual of a minimum cost flow problem (that is, of the form i  j w ij , (i, j) Q), with lower and upper bounds on variables. Let n = P, m = Q, and U be the largest magnitude in the lower and upper bounds of variables. We call this problem the convex cost integer dual network flow problem. In this paper, we describe several applications of the convex cost integer dual network flow problem arising in dialaride transit problems, inverse spanning tree problem, project management, and regression analysis. We develop network flow based algorithms to solve the convex cost integer dual network flow problem. We show that using the Lagrangian relaxation technique, the convex cost integer dual network flow problem can be transformed to a convex cost primal network flow problem where each cost function is a piecewise linear convex function with integer slopes. Its special structure allows the convex cost primal network flow problem to be solved in O(nm log n log(nU)) time using a costscaling algorithm, which is the best available time bound to solve the convex cost integer dual network flow problem.
Mathematical Programming in Data Mining
 Data Mining and Knowledge Discovery
, 1996
"... Mathematical programming approaches to three fundamental problems will be described: feature selection, clustering and robust representation. The feature selection problem considered is that of discriminating between two sets while recognizing irrelevant and redundant features and suppressing them. ..."
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Cited by 26 (3 self)
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Mathematical programming approaches to three fundamental problems will be described: feature selection, clustering and robust representation. The feature selection problem considered is that of discriminating between two sets while recognizing irrelevant and redundant features and suppressing them. This creates a lean model that often generalizes better to new unseen data. Computational results on real data confirm improved generalization of leaner models. Clustering is exemplified by the unsupervised learning of patterns and clusters that may exist in a given database and is a useful tool for knowledge discovery in databases (KDD). A mathematical programming formulation of this problem is proposed that is theoretically justifiable and computationally implementable in a finite number of steps. A resulting kMedian Algorithm is utilized to discover very useful survival curves for breast cancer patients from a medical database. Robust representation is concerned with minimizing trained m...
Networks and Farsighted Stability
 Journal of Economic Theory
"... The main contribution of this paper is to provide a framework in which the notion of farsighted stability for games, introduced by Chwe (1994), can be applied to directed networks. Then, using Chwe's basic result on the nonemptiness of farsightedly stable sets for games, we show that for any give ..."
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Cited by 24 (3 self)
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The main contribution of this paper is to provide a framework in which the notion of farsighted stability for games, introduced by Chwe (1994), can be applied to directed networks. Then, using Chwe's basic result on the nonemptiness of farsightedly stable sets for games, we show that for any given collection of directed networks and any given collection of rules governing network formation, there exists a farsightedly stable directed network.
Polynomial Methods For Separable Convex Optimization In Unimodular Linear Spaces With Applications
 SIAM J. Comput
, 1997
"... We consider the problem of minimizing a separable convex objective function over the linear space given by a system Mx = 0 with M a totally unimodular matrix. In particular, this generalizes the usual minimum linear cost circulation and cocirculation problems in a network and the problems of determi ..."
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Cited by 22 (4 self)
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We consider the problem of minimizing a separable convex objective function over the linear space given by a system Mx = 0 with M a totally unimodular matrix. In particular, this generalizes the usual minimum linear cost circulation and cocirculation problems in a network and the problems of determining the Euclidean distance from a point to the perfect bipartite matching polytope and the feasible flows polyhedron. We first show that the idea of minimum mean cycle canceling originally worked out for linear cost circulations by Goldberg and Tarjan [J. Assoc. Comput. Mach., 36 (1989), pp. 873886.] and extended to some other problems [T. R. Ervolina and S. T. McCormick, Discrete Appl. Math, 46 (1993), pp. 133165], [A. Frank and A. V. Karzanov, Technical Report RR 895M, Laboratoire ARTEMIS IMAG, Universite Joseph Fourier, Grenoble, France, 1992], [T. Ibaraki, A. V. Karzanov, ...