The paper reviews most popular approaches to the development of applied methods of combinatorial optimization. A number of characteristics and criteria are proposed that underlie the classification of approximate algo...
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The paper reviews most popular approaches to the development of applied methods of combinatorial optimization. A number of characteristics and criteria are proposed that underlie the classification of approximate algorithms. The classification continues the previous investigations in combinatorial optimization and allows determining key components of computational schemes used in constructing efficient hybrid metaheuristics.
Optimization problems on graphs with interval parameters are considered, and exponential and polynomial bounds for their computational complexity are obtained. For a certain subclass of polynomially solvable problems,...
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Optimization problems on graphs with interval parameters are considered, and exponential and polynomial bounds for their computational complexity are obtained. For a certain subclass of polynomially solvable problems, two algorithms are proposed-one of them for finding an optimal solution and the other one for finding a suboptimal solution. Sufficient conditions for the statistical efficiency of the algorithm for finding a suboptimal solution are obtained.
The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions have become popular as ways of solving these...
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The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions have become popular as ways of solving these sort of problems. However, they rely on the steepest descent method for local searches. Here, we present an approach that does not depend on a particular local optimization method, and a new discrete filled function with the useful property that a good continuous global optimization algorithm applied to it leads to an approximation of the solution of the nonlinear discrete problem (Theorem 4). Numerical results are given showing the efficiency of the new approach.
Identifying the top-k most frequent elements is one of the many problems associated with data streams analysis. It is a well-known and difficult problem, especially if the analysis is to be performed and maintained up...
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Identifying the top-k most frequent elements is one of the many problems associated with data streams analysis. It is a well-known and difficult problem, especially if the analysis is to be performed and maintained up to date in near real time. Analyzing data streams in time sliding window model is of particular interest as only the most recent, more relevant events are considered. approximate answers are usually adequate when dealing with this problem. This paper presents a new and innovative algorithm, the Filtered Space-Saving with Sliding Window Algorithm (FSW) that addresses this problem by introducing in the Filtered Space Saving ( FSS) algorithm an approximated time sliding window counter. The algorithm provides the top-k list of elements, their frequency and an error estimate for each frequency value within the sliding window. It provides strong guarantees on the results, depending on the elements real frequencies. Experimental results detail performance on real life cases.
Sorting permutations by reversals is one of the most challenging problems related with the analysis of the evolutionary distance between organisms. Genome rearrangement can be done through several operations with biol...
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Sorting permutations by reversals is one of the most challenging problems related with the analysis of the evolutionary distance between organisms. Genome rearrangement can be done through several operations with biological significance, such as block interchange, transposition and reversal, among others;but sorting by reversals, that consists in finding the shortest sequence of reversals to transform one genome into another, came arise as one of the most challenging problems from the combinatorial and algebraic points of view. In fact, sorting by reversal unsigned permutations is an NP-hard problem, for which the question of NP-completeness remains open for more than two decades and for which several interesting combinatorial questions, such as the average number of reversals needed to sort permutations of the same size, remain without solution. In contrast to the unsigned case, sorting by reversals signed permutations belongs to P. In this paper, a standard genetic algorithm for solving the problem of sorting by reversals unsigned permutations is proposed. This approach is based on Auyeung and Abraham's method which uses exact solutions for the signed case in order to build approximate solutions for the unsorted one. Additionally, an improved genetic algorithm is proposed, that in the initial generations applies reversals that simultaneously eliminate two breakpoints, a heuristic mechanism used by several approximation algorithms. As control mechanism for estimating the precision of the results, a correct implementation of an 1.5-approximation algorithm was developed. Also, the results were compared with permutations for which exact solutions are known, such as Gollan's permutations and their inverses. Several experiments with randomly generated permutations were performed and the results showed that in average the precision of the outputs provided by both the standard and improved genetic algorithms overcome the results given by the 1.5-approximation algorithm as
In this paper, we prove a sufficient condition for local optimality to solve the n/1/r(i)/SIGMA-T(i) scheduling problem which is known to be NP-hard. We then define a new dominant subset of schedules on the basis of t...
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In this paper, we prove a sufficient condition for local optimality to solve the n/1/r(i)/SIGMA-T(i) scheduling problem which is known to be NP-hard. We then define a new dominant subset of schedules on the basis of this condition and propose several new approximate algorithms to construct schedules belonging to this subset. Numerical experiments enable us to compare them with classical approximate algorithms.
A new class of algorithms for online packing of rectangles into a strip is proposed and studied. It is proved that the expectation of the unfilled area for this class of algorithms is O(N-2/3) in the standard (for thi...
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A new class of algorithms for online packing of rectangles into a strip is proposed and studied. It is proved that the expectation of the unfilled area for this class of algorithms is O(N-2/3) in the standard (for this type of problems) probabilistic model for N random rectangles.
We make an in-depth study of the known border rank (i.e., approximate) algorithms for the matrix multiplication tensor M-(n,M- 2,M-2) is an element of C-2n circle times C-4 circle times C-2n encoding the multiplicatio...
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We make an in-depth study of the known border rank (i.e., approximate) algorithms for the matrix multiplication tensor M-(n,M- 2,M-2) is an element of C-2n circle times C-4 circle times C-2n encoding the multiplication of an n x 2 matrix by a 2 x 2 matrix.
In this paper we introduce a new dynamic importance sampling propagation algorithm for Bayesian networks. Importance sampling is based on using an auxiliary sampling distribution from which a set of configurations of ...
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In this paper we introduce a new dynamic importance sampling propagation algorithm for Bayesian networks. Importance sampling is based on using an auxiliary sampling distribution from which a set of configurations of the variables in the network is drawn, and the performance of the algorithm depends on the variance of the weights associated with the simulated configurations. The basic idea of dynamic importance sampling is to use the simulation of a configuration to modify the sampling distribution in order to improve its quality and so reducing the variance of the future weights. The paper shows that this can be achieved with a low computational effort. The experiments carried out show that the final results can be very good even in the case that the initial sampling distribution is far away from the optimum. (C) 2004 Elsevier Inc. All rights reserved.
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