基于状态压缩的最长公共上升子序列快速算法

探讨了最长公共上升子序列（LCIS）问题,在前人算法的基础上提出一种高效求解LCIS的动态规划算法。对于LCIS问题,分别使用最长公共子序列（LCS）和最长上升子序列（LIS）相结合的算法、动态规划算法、经过状态压缩的改进动态规划算法进行设计,并对后两种算法进行了实现。设计的状态压缩的动态规划算法,实现了LCIS的快速求解。通过分析这三种算法的时间和空间复杂度,最终提出了时间复杂度为O（mn）、空间复杂度为O（m）或O（n）的基于状态压缩的快速LCIS算法。     

求解最长循环公共子序列问题的两个算法

最长循环公共子序列（LCCS）是两个字符串在所有可能的循环移位操作下能得到的最长公共子序列（LCS）。针对穷举移位量求解LCCS效率过低的问题,设法对候选移位量进行筛选。通过证明循环移位操作对两字符串间LCS长度增量影响的上下限,得到最优移位量的必要条件,从而减小了求解LCCS的枚举量;在此基础上,建立了求解LCCS的迭代方法,只经过少数几次迭代便可消除绝大部分无效候选移位量;此外,还提出一个可在◢O（mn）◣时间复杂度下快速估算LCCS长度的近似算法。大量随机模拟表明,当两字符串间的相似度明显高于随机字符串的相似度时,提出的两种算法表现良好。     

量子绝热近似求解最大割问题的最优解

经典近似算法求解最大割问题时,时间复杂度与图的复杂度呈正相关。为提高求解效率,使用量子绝热近似算法求解无向图最大割问题哈密顿量的基态,其基态对应该问题的最优解。该算法的时间复杂度不依赖于图的顶点个数及边的条数,可以在有限步骤内计算得到最大割解。基于ProjectQ量子软件进行编程模拟,建立由初始哈密顿量线性变化到最大割问题哈密顿量的演化路径,分析该路径下最大割问题哈密顿量期望值的变化,判断算法能否求出最优解。数值分析结果表明,量子绝热近似算法能够以较高准确率计算出最大割解,其求解3个顶点无向图和6个顶点无向稀疏图最大割问题的准确率为0.999 9,求解6个顶点无向完全图最大割问题的准确率为0.969 6。     

面向多目标流水车间调度的多种群多目标遗传算法

针对制造型企业普遍存在的流水车间调度问题,建立了以最小化最迟完成时间和总延迟时间为目标的多目标调度模型,并提出一种基于分解方法的多种群多目标遗传算法进行求解.该算法将多目标流水车间调度问题分解为多个单目标子问题,并分阶段地将这些子问题引入到算法迭代过程进行求解.算法在每次迭代时,依据种群的分布情况选择各子问题的最好解及与其相似的个体分别为当前求解的子问题构造子种群,通过多种群的进化完成对多个子问题最优解的并行搜索.通过对标准测试算例进行仿真实验,结果表明所提出的算法在求解该问题上能够获得较好的非支配解集.     

基于直觉模糊聚类的电子作业抄袭检测研究

对电子作业做分词处理,生成语义单元序列;用动态规划法计算序列最长公共子序列,引入序列空位度概念。将最长公共子序列长度和空位度诱导出的直觉模糊数作为作业相似度模型,自然、合理。基于直觉模糊传递闭包方法对电子作业进行聚类分析。讨论基于直觉模糊聚类的电子作业抄袭检测算法的复杂度,并给出该算法的一个应用实例,结果显示该算法合理、高效。     

一种多序列比对分治算法DCA-ClustalW

多序列比对是生物信息学研究中最基本的一项内容,多序列比对的精确算法是一个NP-hard问题,一般研究者都侧重于设计多序列比对近似算法,最有代表性的近似算法是ClustalW;分而治之是一种重要的算法设计思想,它将复杂问题分割成更简单的子问题来解决,能有效提高算法效率。本文设计了一个DCA-ClustalW算法,对多序列比对问题,同时考虑从纵向和横向两个方面将复杂问题分割成简单易解的子问题,在BaliBase基准数据集上测试表明,该算法是可行的。     

基于图形表示的LCS问题

所谓的LCS（Longest Common Subsequence）问题，就是寻找生物序列的最长公共子序列。传统的算法都是基于字符串的比较。近几年不少学者给出了生物序列的图形表示，本文就利用DNA序列的一种二维图形表示采寻找最长公共子序列。     

基于动态规划求解时间序列DTW中心

中心时间序列表明了一个时间序列集合中的公共特征,是时间序列聚类的重要手段。提出了一个利用动态规划求解两条时间序列DTW中心的方法,即以最小化中心序列到两条样本序列的DTW距离平方和为目标,递归求解最优解。在此基础上,给出了基于中心与样本匹配度的剪枝方法,降低了时间复杂度。并在理论上证明了该方法可以获得最优解。实验结果显示,相比于DBA算法,该算法能够获得更小的DTW距离平方和,并且有更好的鲁棒性。     

求解子集和问题的采样格归约算法

子集和问题是计算机科学中的重要问题,也是构建多种公钥密码体制的基础.提出了采样归约算法,使用随机采样方法降低问题维度,将原问题分解并归约为多个更小规模的格上最短向量,降低了构造格的半径,从而提高求解的效率,得到原问题的精确解或提高近似解的逼近程度.给出了理论上采样归约算法最差情况的成功率.更进一步地,在目标解重量较低的情况下,可以进行分段采样,对问题增加限定条件,提高解题效率.实验结果表明,对于高维度的子集和问题,与CJLOSS等已有的格归约子集和问题方法相比,该算法可以更高效地求解出问题的精确解,而且可以提高近似解的逼近程度,输出近似解的平均长度达到了CJLOSS算法的0.55倍、DR算法的0.64倍.     

图的最大公共连通子图问题研究

图像识别、恶意代码族群特征提取、人工智能中许多应用问题都可以规约为一类图的最大公共连通子图问题。提出了求解简单最大连通子图问题的矩阵方法,定义了图特征相关度和图度序列相关系数的概念,最后结合算例给出了一种求解一般最大公共连通子图问题的贪婪算法,能够快速有效地找到一个尽可能大的公共连通子图。     

Design and Performance Evaluation of Sequence Partition Algorithms

Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications. Also, the distinction between theoretical upper bound and actual solution optimality for realistic instances of an NP-hard problem is a factor in selecting algorithms in practice. We consider the problem of partitioning a sequence of n distinct numbers into minimum number of monotone （increasing or decreasing） subsequences. This problem is NP-hard and the number of monotone subsequences can reach [√2n＋1/1-1/2]in the worst case. We introduce a new algorithm, the modified version of the Yehuda-Fogel algorithm, that computes a solution of no more than [√2n＋1/1-1/2]monotone subsequences in O（n^1.5） time. Then we perform a comparative experimental study on three algorithms, a known approximation algorithm of approximation ratio 1.71 and time complexity O（n^3）, a known greedy algorithm of time complexity O（n^1.5 log n）, and our new modified Yehuda-Fogel algorithm. Our results show that the solutions computed by the greedy algorithm and the modified Yehuda-Fogel algorithm are close to that computed by the approximation algorithm even though the theoretical worst-case error bounds of these two algorithms are not proved to be within a constant time of the optimal solution. Our study indicates that for practical use the greedy algorithm and the modified Yehuda-Fogel algorithm can be good choices if the running time is a major concern.     

Approximating minimum cocolorings

A cocoloring of a graph G is a partition of the vertex set of G such that each set of the partition is either a clique or an independent set in G. Some special cases of the minimum cocoloring problem are of particular interest.We provide polynomial-time algorithms to approximate a minimum cocoloring on graphs, partially ordered sets and sequences. In particular, we obtain an efficient algorithm to approximate within a factor of 1.71 a minimum partition of a partially ordered set into chains and antichains, and a minimum partition of a sequence into increasing and decreasing subsequences.     

CONTOUR: an efficient algorithm for discovering discriminating subsequences

In recent years we have witnessed several applications of frequent sequence mining, such as feature selection for protein sequence classification and mining block correlations in storage systems. In typical applications such as clustering, it is not the complete set but only a subset of discriminating frequent subsequences which is of interest. One approach to discovering the subset of useful frequent subsequences is to apply any existing frequent sequence mining algorithm to find the complete set of frequent subsequences. Then, a subset of interesting subsequences can be further identified. Unfortunately, it is very time consuming to mine the complete set of frequent subsequences for large sequence databases. In this paper, we propose a new algorithm, CONTOUR, which efficiently mines a subset of high-quality subsequences directly in order to cluster the input sequences. We mainly focus on how to design some effective search space pruning methods to accelerate the mining process and discuss how to construct an accurate clustering algorithm based on the result of CONTOUR. We conducted an extensive performance study to evaluate the efficiency and scalability of CONTOUR, and the accuracy of the frequent subsequence-based clustering algorithm.     

Design of an improved quantum-inspired evolutionary algorithm for a transportation problem in logistics systems

Logistics faces great challenges in vehicle schedule problem. Intelligence Technologies need to be developed for solving the transportation problem. This paper proposes an improved Quantum-Inspired Evolutionary Algorithm (IQEA), which is a hybrid algorithm of Quantum-Inspired Evolutionary Algorithm (QEA) and greed heuristics. It extends the standard QEA by combining its principles with some heuristics methods. The proposed algorithm has also been applied to optimize a problem which may happen in real life. The problem can be categorized as a vehicle routing problem with time windows (VRPTW), which means the problem has many common characteristics that VRPTW has, but more constraints need to be considered. The basic idea of the proposed IQEA is to embed a greed heuristic method into the standard QEA for the optimal recombination of consignment subsequences. The consignment sequence is the order to arrange the vehicles for the transportation of the consignments. The consignment subsequences are generated by cutting the whole consignment sequence according to the values of quantum bits. The computational result of the simulation problem shows that IQEA is feasible in achieving a relatively optimal solution. The implementation of an optimized schedule can save much more cost than the initial schedule. It provides a promising, innovative approach for solving VRPTW and improves QEA for solving complexity problems with a number of constraints.     

一种基于用户偏好的协同过滤推荐算法

In this paper, a collaborative filtering recommendation algorithm based on user preference is proposed. First of all, the user similarity is calculated according to the length of the longest common subsequence of different user interest sequences and the num- ber of common subsequences, and then the similarity obtained by this algorithm is weighted and mixed with the similarity obtained by traditional collaborative filtering recommendation algorithm. Project recommendation is completed based on mixed similarity and the possible project score by target users is predicted. Finally, by comparing the average absolute error MAE values of three rec- ommendation algorithms in three data sets of Ciao, Flixster and MovieLens 100K, it is proved that the proposed user collaborative filtering recommendation algorithm (XQCF) has improved the accuracy of the recommendation system.     

大规模图上具有约束的多起点路径规划算法

路径规划查询是图数据上的一个基本问题,在众多的领域都有重要的应用价值。通常在实际问题中查询的路径是具有约束的,例如在外卖配送和共享出行问题中路径具有节点约束,其路径需要满足节点之间的先后关系约束。目前对于具有节点约束的路径查询问题,大多数的工作都在研究单起点的节点约束路径查询,但很难拓展到多起点节点约束问题中。因为具有节点约束的多起点路径查询问题是NP-hard的,所以该问题的大多数已有方法是使用贪心增量处理,但对于处理静态规则集拓展性不足。因此,提出了基于子路径的启发式算法和基于约束集拓展的精确算法,并在真实数据集上验证了算法的有效性。实验结果表明,启发式算法能够给出问题的精确解,而启发式算法能快速给出较好的近似解。     

基于形状特征k-d树的多维时间序列相似搜索

多维时间序列是信息系统中一类重要的数据对象,相似搜索是其应用的一个核心.两个序列(子序列)相似度加以比较的常用方法是:将序列(子序列)转换成空间中的曲线,然后计算曲线间的欧几里德距离.这种方法的主要缺陷是它仅考虑了序列(子序列)间的整体距离关系,而不能体现它们自身的局部变化.针对此问题,提出了一种新的可应用于多维时间序列的快速相似搜索方法.该方法将序列(子序列)的局部变化特性与检索结构(k-d树)结合起来,使得在搜索k-d树的同时实现了序列(子序列)的局部变化匹配,从而极大地提高了查询效率和正确率.实验结果表明了算法的有效性.     

Beam search for the longest common subsequence problem

The longest common subsequence problem is a classical string problem that concerns finding the common part of a set of strings. It has several important applications, for example, pattern recognition or computational biology. Most research efforts up to now have focused on solving this problem optimally. In comparison, only few works exist dealing with heuristic approaches. In this work we present a deterministic beam search algorithm. The results show that our algorithm outperforms the current state-of-the-art approaches not only in solution quality but often also in computation time.     

GOE-概念格基础上的冲突分析共性描述

冲突广泛存在于社会问题中。为了更好地直观展示冲突分析问题,并给出语义描述,受不完备形式背景上三支近似概念分析理论的启发,将冲突表看作三值形式背景,并在其基础上提出了广义三支算子及其逆算子,通过广义三支算子及其逆算子得到对象导出广义三支概念(GOE-概念),并给出其性质,进一步说明所有GOE-概念的集合可以形成GOE-概念格;进而,讨论了GOE-概念格在冲突分析中进行可视化描述的应用,说明每一个GOE-概念的内涵即为在外延所含代理人下的共性描述;最后,研究了对象导出三支近似概念格(OE-近似概念格)与GOE-概念格的关系,进一步表明GOE-概念相较于OE-近似概念,能够更全面更丰富地描述冲突分析的共性信息。     

A fast projection algorithm for sequence data searching

In real life, data often appear in the form of sequences and this form of data is called sequence data. In this paper, a new definition on sequence similarity and a novel algorithm, Projection Algorithm, for sequence data searching are proposed. This algorithm is not required to access every datum in a sequence database. However, it guarantees that no qualified subsequence is falsely rejected. Moreover, the projection algorithm can be extended to match subsequences with different scales. With careful selection of parameters, most of the similar subsequences with different scales can be retrieved. We also show by experiments that the proposed algorithm can outperform the traditional sequential searching algorithm up to 96 times in terms of speed up.