Inapproximability and approximability of maximal tree routing and coloring

Let G be a undirected connected graph. Given g groups each being a subset of V(G) and a number of colors, we consider how to find a subgroup of subsets such that there exists a tree interconnecting all vertices in each subset and all trees can be colored properly with given colors (no two trees sharing a common edge receive the same color); the objective is to maximize the number of subsets in the subgroup. This problem arises from the application of multicast communication in all optical networks. In this paper, we first obtain an explicit lower bound on the approximability of this problem and prove Ω(g^1−ε)-inapproximability even when G is a mesh. We then propose a simple greedy algorithm that achieves performance ratio O√|E(G)|, which matches the theoretical bounds. Supported in part by the NSF of China under Grant No. 70221001 and 60373012.     

企业信息化指数测算方法研究

应用模糊集合论和主成分分析的方法对企业信息化进行了综合评判,引进了一种新的隶属函数对数据进行了无量纲化处理并确定了各指标权重,建立了山东省企业信息化指数模型。利用此方法对 5家企业信息化进行综合评价,得到了满意的结果。     

粗集与神经网络相结合的股票价格预测模型

粗集和神经网络结合反映了人类智能的定性和定量、清晰和隐含、串行和并行相互交叉混合的常规思维机理。本文建立这样一种混合杂交模型用于股票价格波动趋势的预测,通过粗集对数据的二维约简预处理消除了样本中的噪声和冗余,在提高神经网络预测精度的同时降低了学习负担。为了获得最优的预测精度,本文还利用遗传算法进行属性离散化和网络学习。通过对上证综指的实证研究表明,这种混合杂交模型的性能明显优于BP和GA神经网络模型。     

成套产品定价方法研究

在给出成套产品定价的概念的基础上,通过一个简单的算例来说明成套产品定价方法的思想,给出了纯成套产品定价方法的总收益大于产品单卖时的总收益的条件,并给出了混合成套产品定价时最优成套出售的套数k^#存在的区间。     

Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals

Sorting by Reversals (SBR) is one of the most widely studied models of genome rearrangements in computational molecular biology. At present, is the best known approximation ratio achievable in polynomial time for SBR. A very closely related problem, called Breakpoint Graph Decomposition (BGD), calls for a largest collection of edge disjoint cycles in a suitably-defined graph. It has been shown that for almost all instances SBR is equivalent to BGD, in the sense that any solution of the latter corresponds to a solution of the former having the same value. In this paper, we show how to improve the approximation ratio achievable in polynomial time for BGD, from the previously known to for any > 0. Combined with the results in (Caprara, Journal of Combinatorial Optimization, vol. 3, pp. 149–182, 1999b), this yields the same approximation guarantee for n! – O((n – 5)!) out of the n! instances of SBR on permutations with n elements. Our result uses the best known approximation algorithms for Stable Set on graphs with maximum degree 4 as well as for Set Packing where the maximum size of a set is 6. Any improvement in the ratio achieved by these approximation algorithms will yield an automatic improvement of our result.     

Modified BLUEs and BLIEs of the location and scale parameters and the population mean using ranked set sampling

Ranked set sampling (RSS) is a sampling procedure that can be used to improve the cost efficiency of selecting sample units of an experiment or a study. In this paper, RSS is considered for estimating the location and scale parameters a and b>0, as well as the population mean from the family F((x?a)/b). Modified best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) are considered. Numerical computations with different location-scale distributions and different sample sizes are conducted to assess the efficiency of the suggested estimators. It is found that the modified BLIEs are uniformly higher than that of BLUEs for all distributions considered in this study. The modified BLUE and BLIE are more efficient when the underlying distribution is symmetric.     

A new way of quantifying the symmetry of a random variable: Estimation and hypothesis testing

New measures of skewness for real-valued random variables are proposed. The measures are based on a functional representation of real-valued random variables. Specifically, the expected value of the transformed random variable can be used to characterize the distribution of the original variable. Firstly, estimators of the proposed skewness measures are analyzed. Secondly, asymptotic tests for symmetry are developed. The tests are consistent for both discrete and continuous distributions. Bootstrap versions improving the empirical results for moderated and small samples are provided. Some simulations illustrate the performance of the tests in comparison to other methods. The results show that our procedures are competitive and have some practical advantages.     

结构和内容联合提取的XML网页分类研究

针对XML网页特点,重点研究了XML文档结构和内容特征的提取方法,提出了一种基于频繁结构层次空间模型的联合特征提取策略,并给出了结构特征权重和关键词出现的位置及频度权重的计算公式,并根据计算结果提取XML网页特征矩阵,分别就结构、内容联合提取三种情况进行分类测试,通过ROSSETA系统,利用粗糙集优越的属性约简构造文本分类系统,实现XML文档分类。实验表明,该方法分类准确度较高,计算量较小。     

非退化扩散过程极性的充分条件

讨论了多维非退化扩散过程样本轨道的性质,得到了其极性的充分条件     

逻辑函数绝对最小覆盖的改进算法

逻辑函数的绝对最小化算法存在的主要问题是运行时间过长和需要的存储空间过大,本文提出了一个从给定本源蕴源项集合中抽出一个绝对最小覆盖的算法,而时间空间的需求被大大地缩小了。