On the analysis of stochastic divide and conquer algorithms

This paper develops general tools for the analysis of stochastic divide and conquer algorithms. We concentrate on the average performance and the distribution of the running time of the algorithm. As a special example we analyse the average performance and the running time distribution of the (2k + 1)-median version of Quicksort. Online publication October 13, 2000.     

ON THE PARTIAL SUMS OF RESIDUALS IN AUTOREGRESSIVE AND MOVING AVERAGE MODELS

Abstract. The limiting process of partial sums of residuals in stationary and invertible autoregressive moving-average models is studied. It is shown that the partial sums converge to a standard Brownian motion under the assumptions that estimators of unknown parameters are root- n consistent and that innovations are independent and identically distributed random variables with zero mean and finite variance or, more generally, are martingale differences with moment restrictions specified in Theorem 1. Applications for goodness-of-fit and change-point problems are considered. The use of residuals for constructing nonparametric density estimation is discussed.     

A Tabu search algorithm for the network pricing problem

In this paper, we propose an efficient Tabu Search procedure for solving the NP-hard network pricing problem. By exploiting the problem's features, the algorithm allows the near-optimal solution of problem instances that are out of reach of exact combinatorial methods.     

Improved LP-based algorithms for the closest string problem

In a recent paper by Liu et al. [Exact algorithm and heuristic for the closest string problem, Computers & Operations Research 2011;38:1513-20], a polynomial time heuristic procedure is proposed for the closest string problem (CSP). Such heuristic called LDDA_LSS is a combination of a previously published approximation algorithm and local search strategies. This paper points out that an instant algorithm deriving a feasible solution directly from the continuous relaxation solution of a standard ILP formulation of CSP already strongly outperforms LDDA_LSS both in terms of solution quality and computing time. Two core based procedures are then proposed that further improve the results of the instant algorithm. Based on these results, we conclude that such LP-based approaches for their efficiency and simplicity should be used as a benchmark for future heuristics on CSP.     

A regularization method for a Cauchy problem of Laplace's equation in an annular domain

In this paper, we propose a new regularization method based on a finite-dimensional subspace generated from fundamental solutions for solving a Cauchy problem of Laplace's equation in an annular domain. Based on a conditional stability for the Cauchy problem of Laplace's equation, we obtain a convergence estimate under the suitable choice of a regularization parameter and an a-priori bound assumption on the solution. A numerical example is provided to show the effectiveness of the proposed method from both accuracy and stability.     

Combination of non-classical pseudospectral and direct methods for the solution of brachistochrone problem

In this paper, we propose a combination of non-classical pseudospectral and direct methods to find the solution of brachistochrone problem. The method converts the optimal control problem of brachistochrone, into a sequence of quadratic programming problems. To this end, the quasilinearization method is used to replace the nonlinear optimal control problem into a sequence of constrained linear-quadratic optimal control problems; then each of the state variables is approximated by a weighted interpolation function based on the non-classical orthogonal polynomials. The method gives the information of the quadratic programming problems explicitly (the Hessian and the gradient of the cost function). Using this method, the solution of the brachistochrone problem is compared with those in the literature.     

Optimal error estimates of the penalty method for the linearized viscoelastic flows

In this article, optimal error estimates of the penalty method for the linearized viscoelastic flows equations arising in the Oldroyd model are derived. Furthermore, error estimates for the backward Euler time discretization scheme in L ² and H ¹-norms are obtained.     

An iterative algorithm based on the piecewise linear system for solving bilateral obstacle problems

In this paper, we derive the piecewise linear system (PLS) associated with the bilateral obstacle problem and illustrate the equivalence between the linear system and finite-dimensional complementary problem. The existence and the uniqueness of the solution to the PLS are also demonstrated. Based on the PLS, a Picard iterative algorithm is proposed. The convergence analysis is given and examples are presented to verify the effectiveness of the method.     

Decidability and undecidability in cellular automata

We survey results on decidability questions concerning cellular automata. Properties discussed include reversibility and surjectivity and their variants, time-symmetry and conservation laws, nilpotency and other properties of the limit set and the trace, properties chaoticity related such as sensitivity to initial conditions and mixing of the space, and dynamics from finite initial configurations. We also discuss briefly the tiling problem and its variants, and consider the influence of the dimension of the space on the decidability status of the questions.