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Given a graph G=( V, E) with n vertices and m edges, and a subset T of k vertices called terminals, the Edge (respectively, Vertex) Multiterminal Cut problem is to find a set of at most l edges (non-terminal vertices), whose removal from G separates each terminal from all the others. These two problems are NP-hard for k≥3 but well-known to be polynomial-time solvable for k=2 by the flow technique. In this paper, based on a notion farthest minimum isolating cut, we design several simple and improved algorithms for Multiterminal Cut. We show that Edge Multiterminal Cut can be solved in O(2 l kT( n, m)) time and Vertex Multiterminal Cut can be solved in O( k l T( n, m)) time, where T( n, m)= O(min ( n2/3, m1/2) m) is the running time of finding a minimum ( s, t) cut in an unweighted graph. Furthermore, the running time bounds of our algorithms can be further reduced for small values of k: Edge 3-Terminal Cut can be solved in O(1.415 l T( n, m)) time, and Vertex {3,4,5,6}-Terminal Cuts can be solved in O(2.059 l T( n, m)), O(2.772 l T( n, m)), O(3.349 l T( n, m)) and O(3.857 l T( n, m)) time respectively. Our results on Multiterminal Cut can also be used to obtain faster algorithms for Multicut: $O((\min(\sqrt{2k},l)+1)^{2k}2^{l}T(n,m))$ -time algorithm for Edge Multicut and O((2 k) k+ l/2 T( n, m))-time algorithm for Vertex Multicut. [ABSTRACT FROM AUTHOR]

Abstract Recently, an online agglomerative clustering method called AddC (I. D. Guedalia et al . Neural Comput . {\bf 11} (1999), 521--540) was proposed for nonstationary data clustering. Although AddC possesses many good attributes, a vital problem of that method is its sensitivity to noises, which limits its use in real-word applications. In this paper, based on \hbox{kernel-induced} distance measures, a robust online clustering (ROC) algorithm is proposed to remedy the problem of AddC. Experimental results on artificial and benchmark data sets show that ROC has better clustering performances than AddC, while still inheriting advantages such as clustering data in a single pass and without knowing the exact number of clusters beforehand. [ABSTRACT FROM AUTHOR]

This paper investigates the power of local computations on graphs, by considering a classical problem in distributed algorithms, the recognition problem. Formally, we want to compute some topological information on a network of processes, possibly using additional knowledge about the structure of the underlying graph. We propose the notion of recognition with structural knowledge by means of local computations. Then we characterize the graph classes that are recognizable with or without structural knowledge. The characterizations use graph coverings and a distributed enumeration algorithm proposed by A. Mazurkiewicz. Several applications are presented, in particular concerning minor-closed classes of graphs. [ABSTRACT FROM AUTHOR]

In this paper, the uncapacitated facility location problem is considered, A tabu search algorithm for solving this problem is proposed. The algorithm is tested on some standard test problems taken from literature and its performance is compared with the known optimal solutions. Computational results show that the proposed algorithm produces optimal solutions for all test problems, and that it is very efficient in terms of time compared to existing algorithms in the literature. [ABSTRACT FROM AUTHOR]

A possible way to accelerate the execution of a program is to optimize it at compilation time. Some optimizing transformations use additional information obtained by a preliminary analysis of the program. The paper is devoted to the popular method of the analysis of the intermediate program representation called the value numbering method. Several techniques improving the classical algorithm are proposed and the effect the proposed improvements on the execution time of certain programs is analyzed. [ABSTRACT FROM AUTHOR]

The present paper proposes a novel stereo algorithm utilizing multi-sets of reaction–diffusion equations. The problem of detecting a stereo disparity map becomes the segmentation problem, in which the uniqueness assumption and the continuity assumption on disparity distribution are taken into account. A set of reaction–diffusion equations realizes the continuity assumption, while a mutual-inhibition mechanism among the multi-sets realizes the uniqueness one. In addition, each set of equations has a self-inhibition mechanism, which is necessary for the reaction-diffusion equations applied to stereo disparity detection. Performance of the proposed algorithm is evaluated for well-known test stereo images. [ABSTRACT FROM AUTHOR]

This paper is dedicated to location problems on graphs. We propose a linear time algorithm for the 1-median problem on wheel graphs. Moreover, some general results for the 1-median problem are summarized and parametric median problems are investigated. These results lead to a solution method for the 2-median problem on cactus graphs, i.e., on graphs where no two cycles have more than one vertex in common. The time complexity of this algorithm is $$\mathcal O(n^2)$$ , where n is the number of vertices of the graph. [ABSTRACT FROM AUTHOR]

In this paper we introduce an acceleration of gradient descent algorithm with backtracking. The idea is to modify the steplength tk by means of a positive parameter θk, in a multiplicative manner, in such a way to improve the behaviour of the classical gradient algorithm. It is shown that the resulting algorithm remains linear convergent, but the reduction in function value is significantly improved. [ABSTRACT FROM AUTHOR]

Abstract This paper provides an analysis of the behavior of separate-and-conquer or covering rule learning algorithms by visualizing their evaluation metrics and their dynamics in coverage space, a variant of ROC space. Our results show that most commonly used metrics, including accuracy, weighted relative accuracy, entropy, and Gini index, are equivalent to one of two fundamental prototypes: precision, which tries to optimize the area under the ROC curve for unknown costs, and a cost-weighted difference between covered positive and negative examples, which tries to find the optimal point under known or assumed costs. We also show that a straightforward generalization of the m-estimate trades off these two prototypes. Furthermore, our results show that stopping and filtering criteria like CN2s significance test focus on identifying significant deviations from random classification, which does not necessarily avoid overfitting. We also identify a problem with Foils MDL-based encoding length restriction, which proves to be largely equivalent to a variable threshold on the recall of the rule. In general, we interpret these results as evidence that, contrary to common conception, pre-pruning heuristics are not very well understood and deserve more investigation. [ABSTRACT FROM AUTHOR]

The paper considers the problem of constructing a basic iterative scheme for solving systems of linear algebraic equations with unsymmetric and indefinite coefficient matrices. A new GMRES-type algorithm with explicit restarts is suggested. When restarting, this algorithm takes into account the spectral/singular data transferred using orthogonal matrix relations in the so-called QR form, which arise when performing inner iterations of Arnoldi type. The main idea of the algorithm developed is to organize inner iterations and the filtering of directions before restarting in such a way that, from one restart to another, matrix relations effectively accumulate information concerning the current approximate solution and, simultaneously, spectral/singular data, which allow the algorithm to converge with a rate comparable with that of the GMRES algorithm without restarts. Convergence theory is provided for the case of nonsingular, unsymmetric, and indefinite matrices. A bound for the rate of decrease of the residual in the course of inner Arnoldi-type iterations is obtained. This bound depends on the spectral/singular characterization of the subspace spanned by the directions retained upon filtering and is used in developing efficient filtering procedures. Numerical results are provided. Bibliography: 9 titles. [ABSTRACT FROM AUTHOR]

Let f(2m,k) be the Maximum k-diameter of k-regular k-connected graphs on 2m vertices. In this paper we give an algorithm and prove that we can construct k-regular k-connected graphs on 2m vertices with the maximum k-diameter using it. We also prove some known results about f(2m,k) and verify that we can get some unknown values of f(2m,k) by our algorithm. [ABSTRACT FROM AUTHOR]

By means of a gradient strategy, the Moreau-Yosida regularization, limited memory BFGS update, and proximal method, we propose a trust-region method for nonsmooth convex minimization. The search direction is the combination of the gradient direction and the trust-region direction. The global convergence of this method is established under suitable conditions. Numerical results show that this method is competitive to other two methods. [ABSTRACT FROM AUTHOR]

A 0/±1 matrix is balanced if it does not contain a square submatrix with exactly two nonzero entries per row and per column in which the sum of all entries is 2 modulo 4. A 0/1 matrix is balanceable if its nonzero entries can be signed ±1 so that the resulting matrix is balanced. A signing algorithm due to Camion shows that the problems of recognizing balanced 0/±1 matrices and balanceable 0/1 matrices are equivalent. Conforti, Cornuéjols, Kapoor and Vušković gave an algorithm to test if a 0/±1 matrix is balanced. Truemper has characterized balanceable 0/1 matrices in terms of forbidden submatrices. In this paper we give an algorithm that explicitly finds one of these forbidden submatrices or shows that none exists. [ABSTRACT FROM AUTHOR]

Certain modifications are proposed for a numerical algorithm solving the matrix equation X + AX B = C. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from O( n) to O( n) arithmetic operations. [ABSTRACT FROM AUTHOR]

The article discusses a study on a class of correct mathematical operations on prediction and recognition algorithms. It states that the right operations come up in relation to the issue of constructing correct algorithms and that correct operations possess the property of preserving the correctness of the algorithms. It adds that the property is useful in developing procedures of correct training that involves the potential of generating families of correct algorithms. The application of a correct operation reportedly makes it possible to obtain new algorithms in an extended model of algorithms.

We present the results of a computational investigation of solution approaches for the resource constrained elementary shortest path problem ( $\mathcal{RCESPP}$). In particular, the best known algorithms are tested on several problem instances taken from literature. The main aims are to provide a detailed state of the art and to evaluate methods that turn out to be the most promising for solving the problem under investigation. This work represents the first attempt to computationally compare solution approaches for the $\mathcal{RCESPP}$. [ABSTRACT FROM AUTHOR]

An algorithm for optimal grouping blocks of a structured program resource in systems of distributed competing processes is proposed. [ABSTRACT FROM AUTHOR]

An algorithm for the partition of the range of Boolean functions based on the specified threshold value and relation is considered. The algorithm is implemented by means of the PLD-based automatically adjustable structure. The correctness of such an implementation is proved and some of the applications are considered. [ABSTRACT FROM AUTHOR]

We consider the optimal control problem with terminal quality criterion in which the state of a system is described by a set-valued mapping, and an admissible control is a summable function. We describe an algorithm that approximates the admissible control function by a piecewise-constant function and prove theorems on the closeness of the corresponding trajectories and the values of quality criteria. [ABSTRACT FROM AUTHOR]

We consider two-person nonzero-sum game, both in the classical form and in the form of a game with coupled variables. An extra-proximal approach for finding the game’s solutions is suggested and justified. We provide our algorithm with an analysis of its convergence. [ABSTRACT FROM AUTHOR]

Abstract   We present a method to speed up the dynamic program algorithms used for solving the HMM decoding and training problems for discrete time-independent HMMs. We discuss the application of our method to Viterbi’s decoding and training algorithms (IEEE Trans. Inform. Theory IT-13:260–269, 1967), as well as to the forward-backward and Baum-Welch (Inequalities 3:1–8, 1972) algorithms. Our approach is based on identifying repeated substrings in the observed input sequence. Initially, we show how to exploit repetitions of all sufficiently small substrings (this is similar to the Four Russians method). Then, we describe four algorithms based alternatively on run length encoding (RLE), Lempel-Ziv (LZ78) parsing, grammar-based compression (SLP), and byte pair encoding (BPE). Compared to Viterbi’s algorithm, we achieve speedups of Θ(log n) using the Four Russians method, using RLE, using LZ78, using SLP, and Ω(r) using BPE, where k is the number of hidden states, n is the length of the observed sequence and r is its compression ratio (under each compression scheme). Our experimental results demonstrate that our new algorithms are indeed faster in practice. We also discuss a parallel implementation of our algorithms. [ABSTRACT FROM AUTHOR]

Abstract  We derive a numerical scheme to compute invariant manifolds for time-variant discrete dynamical systems, i.e., nonautonomous difference equations. Our universally applicable method is based on a truncated Lyapunov–Perron operator and computes invariant manifolds using a system of nonlinear algebraic equations which can be solved both locally using (nonsmooth) inexact Newton, and globally using continuation algorithms. Compared to other algorithms, our approach is quite flexible, since it captures time-dependent, nonsmooth, noninvertible or implicit equations and enables us to tackle the full hierarchy of strongly stable, stable and center-stable manifolds, as well as their unstable counterparts. Our results are illustrated using a test example and are applied to a population dynamical model and the Hénon map. Finally, we discuss a linearly implicit Euler–Bubnov–Galerkin discretization of a reaction diffusion equation in order to approximate its inertial manifold. [ABSTRACT FROM AUTHOR]

We present a constructive proof for the well-known Ky Fan’s coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh size converges to zero, the sequence of approximations converges to a coincidence point. [ABSTRACT FROM AUTHOR]

A robust structural optimization scheme as well as an optimization algorithm are presented based on the robustness function. Under the uncertainties of the external forces based on the info-gap model, the maximization of the robustness function is formulated as an optimization problem with infinitely many constraints. By using the quadratic embedding technique of uncertainty and the S-procedure, we reformulate the problem into a nonlinear semidefinite programming problem. A sequential semidefinite programming method is proposed which has a global convergent property. It is shown through numerical examples that optimum designs of various linear elastic structures can be found without difficulty. [ABSTRACT FROM AUTHOR]

We consider two variable target value frameworks for solving large-scale nondifferentiable optimization problems. We provide convergence analyses for various combinations of these variable target value frameworks with several direction-finding and step-length strategies including the pure subgradient method, the volume algorithm, the average direction strategy, and a generalized Polyak-Kelley cutting plane method. In addition, we suggest a further enhancement via a projected quadratic-fit line-search whenever any of these algorithmic procedures experiences an improvement in the objective value. Extensive computational results on different classes of problems reveal that these modifications and enhancements significantly improve the effectiveness of the algorithms to solve Lagrangian duals of linear programs, even yielding a favorable comparison against the commercial software CPLEX 8.1. [ABSTRACT FROM AUTHOR]

We investigate issues related to the probe complexity of quorum systems and their implementation in a dynamic environment. Our contribution is twofold. The first regards the algorithmic complexity of finding a quorum in case of random failures. We show a tradeoff between the load of a quorum system and its probe complexity for non adaptive algorithms. We analyze the algorithmic probe complexity of the Paths quorum system suggested by Naor and Wool in [29], and present two optimal algorithms. The first is a non adaptive algorithm that matches our lower bound. The second is an adaptive algorithm with a probe complexity that is linear in the cardinality of the smallest quorum set. We supply a constant degree network in which these algorithms could be executed efficiently. Thus the Paths quorum system is shown to have good balance between many measures of quality. Our second contribution is presenting Dynamic Paths - a suggestion for a dynamic and scalable quorum system, which can operate in an environment where elements join and leave the system. The quorum system could be viewed as a dynamic adaptation of the Paths system, and therefore has low load high availability and good probe complexity. We show that it scales gracefully as the number of elements grows. [ABSTRACT FROM AUTHOR]

A computable structure is said to be n-constructive if there exists an algorithm which, given a finite ?n-formula and a tuple of elements, determines whether that tuple satisfies this formula. A structure is strongly constructive if such an algorithm exists for all formulas of the predicate calculus, and is decidable if it has a strongly constructive isomorphic copy. We give a complete description of relations between n-constructibility and decidability for Boolean algebras of a fixed elementary characteristic. [ABSTRACT FROM AUTHOR]

Abstract Of numerous proposals to improve the accuracy of naive Bayes by weakening its attribute independence assumption, both LBR and Super-Parent TAN have demonstrated remarkable error performance. However, both techniques obtain this outcome at a considerable computational cost. We present a new approach to weakening the attribute independence assumption by averaging all of a constrained class of classifiers. In extensive experiments this technique delivers comparable prediction accuracy to LBR and Super-Parent TAN with substantially improved computational efficiency at test time relative to the former and at training time relative to the latter. The new algorithm is shown to have low variance and is suited to incremental learning. [ABSTRACT FROM AUTHOR]

Parallel merge sort is useful for sorting a large quantity of data progressively. The merge sort should be parallelized carefully since the conventional algorithm has poor performance due to the successive reduction of the number of participating processors by half, and down to one in the last merging stage. The proposed load-balanced merge sort utilizes all processors throughout the computation. It evenly distributes data to all processors in each stage. Thus every processor is forced to work in all phases. Significant performance enhancement has been achieved up to a speedup of (P-1)/log P where P is the number of processors. Experimental results demonstrate a speedup of 9.6 (upper bound of 10.7) on 32-processor Cray T3E when sorting 4M 32-bit integers, and a speed up of 2.3 (upper bound of 2.8) on an 8-node PC cluster. [ABSTRACT FROM AUTHOR]