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.     

The Steiner Tree Problem in Kalmanson Matrices and in Circulant Matrices

We investigate the computational complexity of two special cases of the Steiner tree problem where the distance matrix is a Kalmanson matrix or a circulant matrix, respectively. For Kalmanson matrices we develop an efficient polynomial time algorithm that is based on dynamic programming. For circulant matrices we give an -hardness proof and thus establish computational intractability.     

The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers

Let k 5 be a fixed integer and let m = (k – 1)/2. It is shown that the independence number of a C _k-free graph is at least c ₁[ d(v)^{1/(m – 1)}]^{(m – 1)/m} and that, for odd k, the Ramsey number r(C _k, K _n) is at most c ₂(n ^{m + 1}/log n)^1/m , where c ₁ = c ₁(m) > 0 and c ₂ = c ₂(m) > 0.     

Bayesian analysis of directed graphs data with applications to social networks

Summary.  A fully Bayesian analysis of directed graphs, with particular emphasis on applica- tions in social networks, is explored. The model is capable of incorporating the effects of covariates, within and between block ties and multiple responses. Inference is straightforward by using software that is based on Markov chain Monte Carlo methods. Examples are provided which highlight the variety of data sets that can be entertained and the ease with which they can be analysed.     

Using a Box–Cox transformation in the analysis of longitudinal data with incomplete responses

We analyse longitudinal data on CD4 cell counts from patients who participated in clinical trials that compared two therapeutic treatments: zidovudine and didanosine. The investigators were interested in modelling the CD4 cell count as a function of treatment, age at base-line and disease stage at base-line. Serious concerns can be raised about the normality assumption of CD4 cell counts that is implicit in many methods and therefore an analysis may have to start with a transformation. Instead of assuming that we know the transformation (e.g. logarithmic) that makes the outcome normal and linearly related to the covariates, we estimate the transformation, by using maximum likelihood, within the Box–Cox family. There has been considerable work on the Box–Cox transformation for univariate regression models. Here, we discuss the Box–Cox transformation for longitudinal regression models when the outcome can be missing over time, and we also implement a maximization method for the likelihood, assumming that the missing data are missing at random.     

Proof of Toft's Conjecture: Every Graph Containing No Fully Odd K4 is 3-Colorable

A fully odd K₄ is a subdivision of K₄ such that each of the six edges of the K₄ is subdivided into a path of odd length. In 1974, Toft conjectured that every graph containing no fully odd K₄ can be vertex-colored with three colors. The purpose of this paper is to prove Toft's conjecture.     

基于图上随机游动的 Web 页面布局可用性评价

针对Web页面布局可用性设计中缺乏实用的定量评价模型和方法的问题,根据扫描路径理论,使用视线跟踪法将网络用户在 Web 页面上的浏览行为模型化为注视点在赋权有限图上的随机游动,据此提出新颖实用的基于图上随机游动模型的Web页面布局可用性评价方法 (WLUE-RWG) ,并以淘宝商城和阿里巴巴的商品展示页面为例对其使用过程与效果进行验证,说明模型的可行性与方法的有效性．     

Implementation of new technology: towards greater manufacturing flexibility

Changes in market characteristics over the past several years are forcing firms to eliminate/minimize dependency on costly buffers of capacity, lead time, or inventory. One way to accomplish this is via appropriate adaptation and enhancement of existing technological infrastructure. Recent technological advances present firms with a wide array of alternative technologies. In this paper, we discuss the impact of new technology on the manufacturing environment and the problems associated with its implementation. We present an integrated framework for implementing such technology based on a consistent hierarchy of organizational objectives and a general foundation of constraint theory.     

Multi-objective optimization in partitioning the healthcare system of Parana State in Brazil

Motivated by a proposal of the local authority for improving the existing healthcare system in the Parana State in Brazil, this article presents an optimization-based model for developing a better system for patients by aggregating various health services offered in the municipalities of Parana into some microregions. The problem is formulated as a multi-objective partitioning of the nodes of an undirected graph (or network) with the municipalities as the nodes and the roads connecting them as the edges of the graph. Maximizing the population homogeneity in the microregions, maximizing the variety of medical procedures offered in the microregions, and minimizing the inter-microregion distances to be traveled by patients are considered as three objective functions of the problem. An integer-coded multi-objective genetic algorithm is adopted as the optimization tool, which yields a significant improvement to the existing healthcare system map of the Parana State. The results obtained may have a strong impact on the healthcare system management in Parana. The model proposed here could be a useful tool to aid the decision-making in health management, as well as for better organization of any healthcare system, including those of other Brazilian States.     

基于EMD与DVG的非线性时间序列预测模型及其应用研究

针对具有非线性和不稳定性的时间序列,提出一种结合经验模态分解(EMD)、有向可见图(DVG)网络的动态预测模型。利用经验模态分解将原时间序列分解为多个固有模态函数(IMF),然后对分解后的高频和低频IMF利用快速傅里叶变换得到各自的周期;依据每个周期,从原时间序列的尾部截取长短不一的子序列,然后采用有向可见图算法转换为多个有向网络,利用随机游走在每个有向网络中寻找与时间序列最后一个节点相似的节点;最后,依据平行线法,预测时间序列的下一个数值。原油价格的时间序列是一类典型的具有非线性和不稳定性的序列,利用此模型对WTI原油每日价格进行实证分析。研究结果表明,此模型不但可以有效地预测时间序列的变化趋势,而且具有较高的预测精度。