几个多面体网格剖分问题的NP难度证明

主要讨论了两类多面体网格剖分问题——网格表面单调剖分和地形多面体剖分.首先研究了判定一个多面体表面能否被剖分成k个单调片的问题,通过构造与SAT问题(satisfiability problem)相应的几何模型,证明出该判定问题是NP完全的,而与之对应的最优剖分问题是NP-hard的.然后将证明方法推广到地形多面体剖分的问题:将一个带洞多面体或者简单多面体剖分成最小数量的地形多面体,这两个问题都被证明是NP-hard的.     

区间分析及其在控制理论中的应用

对区间分析理论及其在控制领域的应用进行了综述．首先简单阐述了区间分析的基本原理,包括区间计算、区间Newton法和区间全局优化方法等;然后对区间方法在参数与状态估计、鲁棒控制、智能理论等方面的应用研究成果进行了归纳和总结;最后分析了区间方法在控制理论应用研究中所面临的主要问题,并展望了未来的研究方向．     

Complexity of Some Linear Problems with Interval Data

During the recent years, a number of linear problems with interval data have been proved to be NP-hard. These results may seem rather obscure as regards the ways in which they were obtained. This survey paper is aimed at demonstrating that in fact it is not so, since many of these results follow easily from the recently established fact that for the subordinate matrix norm · ,1 it is NP-hard to decide whether A,1 1 holds, even in the class of symmetric positive definite rational matrices. After a brief introduction into the basic topics of the complexity theory in Section 1 and formulation of the underlying norm complexity result in Section 2, we present NP-hardness results for checking properties of interval matrices (Section 3), computing enclosures (Section 4), solvability of rectangular linear interval systems (Section 5), and linear and quadratic programming (Section 6). Due to space limitations, proofs are mostly only ketched to reveal the unifying role of the norm complexity result; technical details are omitted.     

Ordering of Intervals and Optimization Problems with Interval Parameters

The general problem of comparison of numbers specified by intervals of possible values is considered in connection with optimization of systems with undetermined parameters. The solution of the problem is obtained that uses a measure of proximity of intervals. This solution is extended to any intervals that are arbitrarily located relative to one another.     

A Parser for the Interval Evaluation of Analytical Functions and its Application to Engineering Problems

We have developed a parser which takes as input a file containing the analytical expression of one or more formulas and ranges for each unknown in the formula and returns an interval evaluation of the formula. We describe the use of this parser for solving robotics problems and, in a more general context, for analysing and solving systems of equations.     

Greatest Lower Bounds of System Failure Probability on a Time Interval Under Incomplete Information About the Distribution Function of Time to Failure

The authors solve problems of finding the greatest lower bounds for the probability F (\( \upsilon \)) - F (u),0< u < \( \upsilon \) < ∞, in the set of distribution functions F (x) of nonnegative random variables with unimodal density with mode m, u < m < \( \upsilon \), and fixed two first moments.     

Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems

Interval type-2 fuzzy sets (T2 FS) play a central role in fuzzy sets as models for words and in engineering applications of T2 FSs. These fuzzy sets are characterized by their footprints of uncertainty (FOU), which in turn are characterized by their boundaries-upper and lower membership functions (MF). In this two-part paper, we focus on symmetric interval T2 FSs for which the centroid (which is an interval type-1 FS) provides a measure of its uncertainty. Intuitively, we anticipate that geometric properties about the FOU, such as its area and the center of gravities (centroids) of its upper and lower MFs, will be associated with the amount of uncertainty in such a T2 FS. The main purpose of this paper (Part 1) is to demonstrate that our intuition is correct and to quantify the centroid of a symmetric interval T2 FS, and consequently its uncertainty, with respect to such geometric properties. It is then possible, for the first time, to formulate and solve forward problems, i.e., to go from parametric interval T2 FS models to data with associated uncertainty bounds. We provide some solutions to such problems. These solutions are used in Part 2 to solve some inverse problems, i.e., to go from uncertain data to parametric interval T2 FS models (T2 fuzzistics)     

Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 2, Inverse Problems

In Part 1 of this two-part paper, we bounded the centroid of a symmetric interval type-2 fuzzy set (T2 FS), and consequently its uncertainty, using geometric properties of its footprint of uncertainty (FOU). We then used these bounds to solve forward problems, i.e., to go from parametric interval T2 FS models to data. The main purpose of the present paper is to formulate and solve inverse problems, i.e., to go from uncertain data to parametric interval T2 FS models, which we call type-2 fuzzistics. Given interval data collected from people about a phrase, and the inherent uncertainties associated with that data, which can be described statistically using the first- and second-order statistics about the end-point data, we establish parametric FOUs such that their uncertainty bounds are directly connected to statistical uncertainty bounds. These results should find applicability in computing with words     

How to Compute Interval Inclusions of Geodetic Coordinates from Interval Inclusions of Cartesian Coordinates

In satellite geodesy the position of a point P is usually determined by computing its coordinate vector x with respect to an earth-fixed Cartesian coordinate system S. S is chosen such that a rotational ellipsoid E, closely approximating the surface of the earth, has normal form with respect to S. Since the geodetic coordinates of P with respect to E (ellipsoidal latitude , ellipsoidal longitude , and ellipsoidal height h) describe the location of P with respect to the surface of the earth much better than x, a frequently appearing problem is to compute , , and h from x.In practice this problem is solved by iterative methods, the convergence properties of which are not analyzed in detail but for which fast (numerical) convergence is observed for points near to E.In the present paper a theoretically well founded new method is developed, working for all P having a unique nearest point in E.In addition it will be shown that the new method can be implemented such that interval inclusions for , , and h can be computed from interval inclusions of the components of x.     

Parallel Algorithms for Maximum Matching in Complements of Interval Graphs and Related Problems

Given a set of n intervals representing an interval graph, the problem of finding a maximum matching between pairs of disjoint (nonintersecting) intervals has been considered in the sequential model. In this paper we present parallel algorithms for computing maximum cardinality matchings among pairs of disjoint intervals in interval graphs in the EREW PRAM and hypercube models. For the general case of the problem, our algorithms compute a maximum matching in O( log ³ n) time using O(n/ log ² n) processors on the EREW PRAM and using n processors on the hypercubes. For the case of proper interval graphs, our algorithm runs in O( log n ) time using O(n) processors if the input intervals are not given already sorted and using O(n/ log n ) processors otherwise, on the EREW PRAM. On n -processor hypercubes, our algorithm for the proper interval case takes O( log n log log n ) time for unsorted input and O( log n ) time for sorted input. Our parallel results also lead to optimal sequential algorithms for computing maximum matchings among disjoint intervals. In addition, we present an improved parallel algorithm for maximum matching between overlapping intervals in proper interval graphs. Received November 20, 1995; revised September 3, 1998.     

Kolmogorov's Contributions to the Foundations of Probability

Andrei Nikolaevich Kolmogorov was the foremost contributor to the mathematical and philosophical foundations of probability in the twentieth century, and his thinking on the topic is still potent today. In this article we first review the three stages of Kolmogorov's work on the foundations of probability: (1) his formulation of measure-theoretic probability, 1933; (2) his frequentist theory of probability, 1963; and (3) his algorithmic theory of randomness, 1965–1987. We also discuss another approach to the foundations of probability, based on martingales, which Kolmogorov did not consider.     

Greatest Lower Bound of System Failure Probability on a Special Time Interval Under Incomplete Information About the Distribution Function of the Time to Failure of the System

The author solves the problem of finding greatest lower bounds for the probability F (??) – F (u),0 < u <, ?? < ∞, where ( u= m-{upsigma}_{mu}3sqrt{3},kern0.5em upupsilon = m+{upsigma}_{mu}3sqrt{3},kern0.5em mathrm{and}kern0.5em {upsigma}_{mu} ) is a fixed dispersion in the set of distribution functions F (x) of non-negative random variables with unimodal differentiable density with mode m and two first fixed moments μ ₁ and μ ₂. The case is considered where the mode coincides with the first moment: m = μ ₁. The greatest lower bound of all possible greatest lower bounds for this problem is obtained and it is nearly one, namely, 0.98430.     

On a Refined Analysis of Some Problems in Interval Arithmetic Using Real Number Complexity Theory

We study some problems in interval arithmetic treated in Kreinovich et al. [13]. First, we consider the best linear approximation of a quadratic interval function. Whereas this problem (as decision problem) is known to be NP-hard in the Turing model, we analyze its complexity in the real number model and the analogous class NP . Our results substantiate that most likely it does not any longer capture the difficulty of NP in such a real number setting. More precisely, we give upper complexity bounds for the approximation problem for interval functions by locating it in (a real analogue of). This result allows several conclusions: the problem is not (any more) NP -hard under so called weak polynomial time reductions and likely not to be NP -hard under (full) polynomial time reductions; for fixed dimension the problem is polynomial time solvable; this extends the results in Koshelev et al. [12] and answers a question left open in [13].We also study several versions of interval linear systems and show similar results as for the approximation problem.Our methods combine structural complexity theory with issues from semi-infinite optimization theory.     

动态概率探测解决Chord断环问题

Chord环是目前常见的一种基于分布式哈希表的P2 Poverlay模型,在该模型上可承载即时通讯、语音、视频等多种业务。Chord自身机制提供良好的路由算法并支持动态节点加入退出,然而由于网络震荡导致的Chord断环在自适应系统中是一个难以解决的问题,提出了一种动态概率探测对Chord断环是一种简单高效的解决方法。动态概率探测不依赖于环上节点规模和初始探测概率,并可有效控制单点负载和探测断环引入的额外通讯负载。     

An Application of Interval Methods to Stock Market Forecasting

Stock market forecasting has been a challenging financial research topic for decades. In the literature, there are numerous results based on point methods. However, poor forecasting quality has been a continuous problem. Motivated by the fact that financial data varies within intervals, we apply interval methods on a well known stock pricing model [3] to predict stock market variability as intervals. Empirical results obtained with a few different approaches in this paper consistently suggest that interval forecasts have better overall quality than traditional point forecasts.