粗糙集的属性约简是一个NP难问题,目前尚无高效的算法.基于集合理论,提出了关系积概念和基于关系积的属性约简算法,把决策表的属性约简过程转化为关系积的运算,减小了对决策表的扫描次数,提高了属性约简的效率;算法采用自底向上和宽度优先的搜索策略,可确保找到最小属性约简集.结合实例,给出了算法的具体实现

单机器调度问题是研究工件在多道工序进行加工的加工活动排序的组合最优化问题．由于调度问题中绝大多数属于NP-难类问题，不存在有效的最优求解算法．针对用智能优化算法—遗传算法求解单机器调度问题中交叉率和变异率难以确定的问题，设计了一种模糊算法以便自动确定交叉率和变异率．通过数值实验，嵌入模糊规则的遗传算法比简单的遗传算法要好，说明在实际生产中，此算法具有强大的发展前途．

用SRN网为过程控制计算机热备系统建立了可用性评价模型,综合考虑盘阵共享和镜像共享两种方式,并利用SP-NP软件包对数据进行分析和仿真,仿真结果为可用性评价提供了定量指标.研究结果表明:在同等条件下使用镜像共享方式比盘阵共享方式提高系统可用性更显著;缩短故障发现时间,加快系统修复速度,可有效提高系统可用性

南京大学：《计算机问题求解》课程教学资源（PPT课件讲稿）NP完全理论初步

香港中文大学：《Topics in Theoretical Computer Science》课程教学资源（PPT课件讲稿）Lecture 5 NP-Complete problems

Boron (B) Aluminum (Al) Gallium (Ga) Indium (In) Thallium (Tl) ns2np1 §15-1 Boron and its compounds §15-2 Aluminium and its compounds §15-3 Gallium subgroup

香港中文大学：《Design and Analysis of Algorithms》课程教学资源（PPT课件讲稿）Week 10 NP-completeness

1 The Role of Algorithms in Computing 2 Getting Started 3 Growth of Functions 4 Divide-and-Conquer 5 Probabilistic Analysis and Randomized Algorithms 6 Heapsort 7 Quicksort 8 Sorting in Linear Time 9 Medians and Order Statistics 10 Elementary Data Structures 11 Hash Tables 12 Binary Search Trees 13 Red-Black Trees 14 Augmenting Data Structures 15 Dynamic Programming 16 Greedy Algorithms 17 Amortized Analysis 18 B-Trees 19 Fibonacci Heaps 20 van Emde Boas Trees 21 Data Structures for Disjoint Sets 22 Elementary Graph Algorithms 23 Minimum Spanning Trees 24 Single-Source Shortest Paths 25 All-Pairs Shortest Paths 26 Maximum Flow 27 Multithreaded Algorithms 28 Matrix Operations 29 Linear Programming 30 Polynomials and the FFT 31 Number-Theoretic Algorithms 32 String Matching 33 Computational Geometry 34 NP-Completeness 35 Approximation Algorithms

The halting problem is undecidable Decidability

Signal Model Matched Filter Review: NP theorem Development of the Detector Performance of Matched Filter Generalized Matched Filter Multiple Signal M-ary Detector