基于立方体染色的排课表模型

根据立方体染色思想,建立排课表模型,引入关联锁原理,将排课表约束条件转化为立方体点线面关系,增强该模型的收敛性,从而更好地解决排课问题。分析结果表明,在教师、课程、学生等信息已知的情况下,该模型可给出教学资源消耗的最小值,达到合理利用教学资源的目的。     

一种提取目标图像最小外接矩形的快速算法

在图像分类与识别算法研究中,目标几何特征的提取通常需要计算目标图像的最小外接矩形以获取长、宽等属性。针对该特点,提出一种利用顶点链码与离散格林理论相结合的方式提取目标图像的最小外接矩形的算法。该算法只需根据顶点链中垂直或水平方向上的点坐标即可求出目标的面积、形心和主轴。基于顶点链码和离散格林的主轴法和旋转法可快速求出目标的最小外接矩形。实验结果表明,旋转法的运算速度是现有算法的2倍左右,主轴法的速度又比旋转法快速2倍左右。     

基于几何不变量的直线匹配方法

针对目前直线匹配算法大多基于直线段支持区域的几何特性、灰度特性,但这些特性又极易受外界因素干扰造成匹配失败的情况,提出了基于直线几何不变量的匹配方法,该方法在无任何已知条件的情况下,运用叉积符号、点的线束交比不变量进行直线匹配。对于各个视点图像,采用Hough变换提取直线间交点集,再采用Graham扫描法构造一个最小的凸包,并通过匹配凸包顶点的交比序列来建立点与点的对应关系,选取其中一个对应关系完成直线的匹配。实验结果表明,该方法鲁棒性较好,具有广泛的应用性。     

基于子图的随机图点覆盖2度点核化研究

点覆盖问题虽然可以在参数计算理论的架构内求精确解,但是目前在理论及应用上有一定的局限性.根据不同度的顶点之间及顶点与边的关系,提出随机图参数化点覆盖问题的d-核化可决策性及2度点三角形予图的计数方法;通过研究子图对顶点的共享关系,分析2度顶点核化过程中核及度分布演变的动态过程,得出随机图2度点核化强度与2度点概率关系及2度点核化可决策性的两个推论:2度点核化算法对2度点分布概率约为0.75的随机图的核化强度最高;对顶点度概率分布为φ(χ)的随机图的参数化点覆盖问题(G,k),当k小于某一与φ(х)有关的值时,它是2-核化可决策的.仿真结果证实,该理论能够把握2度点核化的内在机制,提供随机图上这一NP完全问题的求解方法,也为参数计算在已知度分布的一类不确定问题中的应用提供了可能.     

一种混合化学反应优化算法求解最小顶点覆盖问题

最小顶点覆盖问题是组合最优化问题,在实际应用中有较广泛的应用,是一个NP难问题。论文针对最小顶点覆盖问题给出了一种混合化学反应优化求解算法。首先根据无向图的邻接矩阵表示法,设计了参与化学化反应的分子编码和目标函数;同时把贪心算法思想创造性地融入到化学反应优化算法的四个重要反应算子中,以加快局部较优解的搜索过程;最后通过模拟化学反应中分子势能趋于稳定的过程,在问题的解空间中搜索其最优解。模拟实验结果表明,该算法对于求解无向图的最小顶点覆盖问题是有效的,并且在求解效率等方面有一定的改善。     

Linear programming based approximation algorithms for feedback set problems in bipartite tournaments

We consider the feedback vertex set and feedback arc set problems on bipartite tournaments. We improve on recent results by giving a 2-approximation algorithm for the feedback vertex set problem. We show that this result is the best that we can attain when using optimal solutions to a certain linear program as a lower bound on the optimal value. For the feedback arc set problem on bipartite tournaments, we show that a recent 4-approximation algorithm proposed by Gupta (2008) [8] is incorrect. We give an alternative 4-approximation algorithm based on an algorithm for the feedback arc set on (non-bipartite) tournaments given by van Zuylen and Williamson (2009) [14].     

通用扫描线多边形填充算法

传统的扫描线多边形填充算法只适用于水平扫描线的逐行填充。文章提出通用扫描线多边形填充算法,该算法可以有效地解决任意间距、任意倾角的扫描线对多边形的填充问题。通用扫描线多边形算法采用了坐标变换、浮点数舍入策略等重要方法。顶点扫描线号是该算法中的核心概念。     

A constraint programming approach to cutset problems

We consider the problem of finding a cutset in a directed graph G=(V,E)$G=(V,E)$, i.e., a set of vertices that cuts all cycles in G  . Finding a cutset of minimum cardinality is NP-hard. There exist several approximate and exact algorithms, most of them using graph reduction techniques. In this paper, we propose a constraint programming approach to cutset problems and design a global constraint for computing cutsets. This cutset constraint is a global constraint over boolean variables associated to the vertices of a given graph and states that the subgraph restricted to the vertices having their boolean variable set to true is acyclic. We propose a filtering algorithm based on graph contraction operations and inference of simple boolean constraints, that has a linear time complexity in O(|E|+|V|)$O(|E|+|V|)$. We discuss search heuristics based on graph properties provided by the cutset constraint, and show the efficiency of the cutset constraint on benchmarks of the literature for pure minimum cutset problems, and on an application to log-based reconciliation problems where the global cutset constraint is mixed with other boolean constraints.     

Finding a minimal cover for binary images: An optimal parallel algorithm

Given a black-and-white image, represented by an array of n × n binary-valued pixels, we wish to cover the black pixels with aminimal set of (possibly overlapping) maximal squares. It was recently shown that obtaining aminimum square cover for a polygonal binary image with holes is NP-hard. We derive an optimal parallel algorithm for theminimal square cover problem, which for any desired computation timeT in [logn,n] runs on an EREW-PRAM with (n/T) processors. The cornerstone of our algorithm is a novel data structure, the cover graph, which compactly represents the covering relationships between the maximal squares of the image. The size of the cover graph is linear in the number of pixels. This algorithm has applications to problems in VLSI mask generation, incremental update of raster displays, and image compression.The research reported here forms part of the author's doctoral dissertion, submitted to Cornell University in May 1989. This work was partially supported by NSF Grant DC1-86-02256, IBM Agreement 12060043, and ONR Contract N00014-83-K-0640. A preliminary version of this paper was presented at the 26th Annual Allerton Conference on Communications, Control, and Computing, Monticello, IL, September 28–30, 1988.