Results 1  10
of
271
A PolynomialTime Approximation Algorithm for the Permanent of a Matrix with NonNegative Entries
 JOURNAL OF THE ACM
, 2004
"... We present a polynomialtime randomized algorithm for estimating the permanent of an arbitrary n ×n matrix with nonnegative entries. This algorithm—technically a “fullypolynomial randomized approximation scheme”—computes an approximation that is, with high probability, within arbitrarily small spec ..."
Abstract

Cited by 427 (27 self)
 Add to MetaCart
(Show Context)
We present a polynomialtime randomized algorithm for estimating the permanent of an arbitrary n ×n matrix with nonnegative entries. This algorithm—technically a “fullypolynomial randomized approximation scheme”—computes an approximation that is, with high probability, within arbitrarily small specified relative error of the true value of the permanent.
A comparative study of energy minimization methods for Markov random fields
 IN ECCV
, 2006
"... One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Ran ..."
Abstract

Cited by 416 (36 self)
 Add to MetaCart
(Show Context)
One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Random Fields (MRF’s), the resulting energy minimization problems were widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the topperforming stereo methods. Unfortunately, most papers define their own energy function, which is minimized with a specific algorithm of their choice. As a result, the tradeoffs among different energy minimization algorithms are not well understood. In this paper we describe a set of energy minimization benchmarks, which we use to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods—graph cuts, LBP, and treereweighted message passing—as well as the wellknown older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching and interactive segmentation. We also provide a generalpurpose software interface that allows vision researchers to easily switch between optimization methods with minimal overhead. We expect that the availability of our benchmarks and interface will make it significantly easier for vision researchers to adopt the best method for their specific problems. Benchmarks, code, results and images are available at
Connectionist Learning Procedures
 ARTIFICIAL INTELLIGENCE
, 1989
"... A major goal of research on networks of neuronlike processing units is to discover efficient learning procedures that allow these networks to construct complex internal representations of their environment. The learning procedures must be capable of modifying the connection strengths in such a way ..."
Abstract

Cited by 409 (9 self)
 Add to MetaCart
A major goal of research on networks of neuronlike processing units is to discover efficient learning procedures that allow these networks to construct complex internal representations of their environment. The learning procedures must be capable of modifying the connection strengths in such a way that internal units which are not part of the input or output come to represent important features of the task domain. Several interesting gradientdescent procedures have recently been discovered. Each connection computes the derivative, with respect to the connection strength, of a global measure of the error in the performance of the network. The strength is then adjusted in the direction that decreases the error. These relatively simple, gradientdescent learning procedures work well for small tasks and the new challenge is to find ways of improving their convergence rate and their generalization abilities so that they can be applied to larger, more realistic tasks.
On the complexity of local search
 Proc. of 22nd ACM Symp. on Theory of Computing (STOC
, 1990
"... We investigate the complexity of finding locally optimal solutions to NPhard combinatorial optimization problems. Local optimality arises in the context of local search algorithms, which try to find improved solutions by considering perturbations of the current solution (“neighbors ” of that solut ..."
Abstract

Cited by 229 (9 self)
 Add to MetaCart
We investigate the complexity of finding locally optimal solutions to NPhard combinatorial optimization problems. Local optimality arises in the context of local search algorithms, which try to find improved solutions by considering perturbations of the current solution (“neighbors ” of that solution). If no neighboring solution is better than the current solution, it is locally optimal. Finding locally optimal solutions is presumably easier than finding optimal solutions. Nevertheless, many popular local search algorithms are based on neighborhood structures for which locally optimal solutions are not known to be computable in polynomial time, either by using the local search algorithms themselves or by taking some indirect route. We define a natural class PLS consisting essentially of those local search problems for which local optimality can be verified in polynomial time, and show that there are complete problems for this class. In particular, finding a partition of a graph that is locally optimal with respect to the wellknown KernighanLin algorithm for graph partitioning is PLScomplete, and hence can be accomplished in polynomial time only if local optima can be found in polynomial time for all local search problems in PLS. 0 1988 Academic Press, Inc. 1.
Variable neighborhood search: Principles and applications
, 2001
"... Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using an ..."
Abstract

Cited by 200 (15 self)
 Add to MetaCart
Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a twolevel VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear
Surrogate time series
 PHYSICA D
, 2000
"... Before we apply nonlinear techniques, e.g. those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified by the data. While many processes in nature seem very unlikely a priori to be linear, the possible n ..."
Abstract

Cited by 166 (0 self)
 Add to MetaCart
Before we apply nonlinear techniques, e.g. those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified by the data. While many processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains. The main limitation, which lies in the interpretability of the test results, will be illustrated through instructive case studies. We will also discuss some implementational aspects of the realisation of these methods in
A local search approximation algorithm for kmeans clustering
, 2004
"... In kmeans clustering we are given a set of n data points in ddimensional space ℜd and an integer k, and the problem is to determine a set of k points in ℜd, called centers, to minimize the mean squared distance from each data point to its nearest center. No exact polynomialtime algorithms are kno ..."
Abstract

Cited by 113 (1 self)
 Add to MetaCart
In kmeans clustering we are given a set of n data points in ddimensional space ℜd and an integer k, and the problem is to determine a set of k points in ℜd, called centers, to minimize the mean squared distance from each data point to its nearest center. No exact polynomialtime algorithms are known for this problem. Although asymptotically efficient approximation algorithms exist, these algorithms are not practical due to the very high constant factors involved. There are many heuristics that are used in practice, but we know of no bounds on their performance. We consider the question of whether there exists a simple and practical approximation algorithm for kmeans clustering. We present a local improvement heuristic based on swapping centers in and out. We prove that this yields a (9 + ε)approximation algorithm. We present an example showing that any approach based on performing a fixed number of swaps achieves an approximation factor of at least (9 − ε) in all sufficiently high dimensions. Thus, our approximation factor is almost tight for algorithms based on performing a fixed number of swaps. To establish the practical value of the heuristic, we present an empirical study that shows that, when combined with
Interdisciplinary application of nonlinear time series methods
 Phys. Reports
, 1998
"... This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situatio ..."
Abstract

Cited by 88 (4 self)
 Add to MetaCart
(Show Context)
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.
A "Memetic" Approach for the Traveling Salesman Problem Implementation of a Computational Ecology for Combinatorial Optimization on MessagePassing Systems
 IN PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON PARALLEL COMPUTING AND TRANSPUTER APPLICATIONS
, 1992
"... In this paper we present an approach for global combinatorial optimization applied to the TSP which combines local search heuristics with a populationbased strategy. Due to its intrinsic parallelism and the inherent asynchronicity of the method it is specially appealing for MIMD messagepassing par ..."
Abstract

Cited by 76 (8 self)
 Add to MetaCart
In this paper we present an approach for global combinatorial optimization applied to the TSP which combines local search heuristics with a populationbased strategy. Due to its intrinsic parallelism and the inherent asynchronicity of the method it is specially appealing for MIMD messagepassing parallel computers, such as those constructed from transputers. The approach is similar to that used by Muhlenbein [14] [15] [16], Brown et al. [1], GorgesSchleuter [3] and work performed by the Dynamics of Computation Group at Xerox PARC [4]. We consider them as prototype examples of "memetic" algorithms in the sense described in Ref. [12] (see also Ref. [5]). A preliminary description of our work can also be found in Ref. [17].
Molecular Modeling Of Proteins And Mathematical Prediction Of Protein Structure
 SIAM Review
, 1997
"... . This paper discusses the mathematical formulation of and solution attempts for the socalled protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possib ..."
Abstract

Cited by 61 (5 self)
 Add to MetaCart
(Show Context)
. This paper discusses the mathematical formulation of and solution attempts for the socalled protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possible pathways to folding and unfolding, including the stability of the folded protein. From a mathematical point of view, there are several main sides to the static problem:  the selection of an appropriate potential energy function;  the parameter identification by fitting to experimental data; and  the global optimization of the potential. The dynamic problem entails, in addition, the solution of (because of multiple time scales very stiff) ordinary or stochastic differential equations (molecular dynamics simulation), or (in case of constrained molecular dynamics) of differentialalgebraic equations. A theme connecting the static and dynamic aspect is the determination and formation of...