A Generalization of a Lower Bound Technique due to Fredman and Saks

{In a seminal paper of 1989, Fredman and Saks proved lower bounds for some important data-structure problems in the cell probe model. In particular, lower bounds were established on worst-case and amortized operation cost for the union-find problem and the prefix sum problem. The goal of this paper is to turn their proof technique into a general tool that can be applied to different problems and computational models. To this end we define two quantities: Output Variability depends only on the model of computation. It indicates how much variation can be found in the results of a program with certain resource bounds. This measures in some sense the power of a model. Problem Variability characterizes in a similar sense the difficulty of the problem. } Our Main Theorem shows that by comparing a model's output variability to a problem's problem variability, lower bounds on the complexity of solving the problem on the given model may be inferred. The theorem thus shows how to separate the analysis of the model of computation from that of the problem when proving lower bounds. We show how the results of Fredman and Saks fit our framework by computing the output variability of the cell probe model and the problem variability for problems considered in their paper. This allows us to reprove their lower bound results, and slightly extend them. The main purpose of this paper though is to present the generalized technique. Received January 25, 1999; revised July 30, 1999.     

WWW上路径模式发掘的研究

本文从互连网发展的趋势入手,对路径模式发掘进行了研究。先简要介绍数据库发掘的概况及网上数据发掘的特点,后结合关联法和组合概率法,并以算法和实例详细对之进行分析。     

Further remarks for the matrix type-B codes

Different philosophies lie behind the detecting and correcting error patterns in a real communication channel. The sceptic points in choosing an efficient code, specifically the matrix type-B code, were pointed out in Refs. 1 and 2.Some more points are shown here. As a result the matrix type-B code is found to be a best choice. Some more theoretical aspects for this code are also given. These are useful for the realization and testing of an encoding-decoding algorithm with IC's used in a unique way for its implementation.     

硝铵装置降膜蒸发存在问题与改进措施

对我公司硝铵装置降膜蒸发工序存在的问题进行分析 ,并通过技术改进 ,使干燥洗涤液全部返回系统 ,造粒塔粘塔问题得到缓解 ,取得可观的经济效益和环保效益     

引大总干渠先明峡倒虹吸水平管段复位施工方法

引大入秦工程总干渠先明峡倒虹吸管水平段钢管因温度变化引起上下游伸缩节的预留伸缩量发生了较大的变化,造成支承环的底座与支墩上的四氟滑块产生了较大错位,支墩出现了偏心受压,大部分四氟滑块出现断裂、脱胶和翘曲等破坏。通过水平管段支承环底座的摩阻力、伸缩节橡胶棒摩阻力计算,水平管段采用箱型定向滑动导轨和滑动钢球的复位措施、施工方法、步骤。采用该施工方法复位后,工程运行情况良好。     

小流域设计洪水计算方法的探讨

利用实例对各常用设计洪水流量计算方法进行比较分析,指出各方法的特点。     

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.     

Computing Green's function of the initial-boundary value problem for the wave equation in a layered cylinder

A new analytical method for the approximate computation of the time-dependent Green's function for the initial-boundary value problem of the three-dimensional wave equation on multi-layered bounded cylinder is suggested in this paper. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients, and an approximate computation of Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of the derived eigenfunctions. The computational experiment confirms the robustness of the method.     

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.