最长路径问题研究进展

最长路径问题是著名的NP难问题,在生物信息学等领域中有着重要的应用.参数计算理论产生后,参数化形式的k-Path问题成了研究的热点.介绍了现有求解最长路径问题的几种算法,包括近似算法、参数化算法和特殊图的多项式时间算法;着重分析和比较了参数化算法中利用着色、分治和代数法研究k-Path问题的最新结果.最后,提出了该问题的进一步研究方向.     

实例簇驱动的图结构聚类参数计算算法

pSCAN算法的聚类结果受密度约束参数和相似度阈值参数的影响,如果用户提供的聚类参数得到的聚类结果无法满足需求,那么用户可以通过实例簇表达自己的聚类需求。针对实例簇表达聚类查询需求的问题,提出一种实例簇驱动的图结构聚类参数计算算法PART及其改进算法ImPART。首先,分析两个聚类参数对聚类结果的影响,并提取实例簇的相关子图;其次,对相关子图进行分析得到密度约束参数的可行区间,并根据当前密度约束参数和节点之间的结构相似度将实例簇内节点划分为核心节点和非核心节点;最后,依据节点划分结果计算出当前密度约束参数对应的最优相似度阈值参数,并在相关子图上对得到的参数进行验证和优化,直到得到满足实例簇需求的聚类参数。在真实数据集上的实验结果表明,所提算法能够为用户实例簇返回一组有效参数,且所提改进算法ImPART的运行时间比PART缩短了20%以上,能够快速有效地为用户返回满足实例簇要求的最优聚类参数。     

基于编辑图的XML文档相似性研究

目前关于XML文档相似性算法有很多种,其中基于编辑距离的方法是很重要的一类。目前已发表的基于编辑距离的算法中,编辑图算法由于其计算高效率的特点成为研究的出发点。首先介绍了编辑图算法的思想,由于它在计算过程中对同层兄弟节点的顺序有很强的依赖性,因此不能准确有效地比较数据无序的数据中心的XML文档相似性。针对该问题,在编辑图算法思想的基础上,结合路径算法的思想提出拆分编辑图算法。实验结果表明,拆分编辑图算法降低了编辑图算法中对兄弟节点次序的依赖性,更适合于数据中心的XML文档相似性比较,而且所得结果更加准确有效。     

基于标识的特征造型原型系统的研究与实现

从特征造型软件开发的角度对参数化特征造型的一些关键技术进行了研究，并在ACIS几何平台上开发了一个参数化特征造型原型系统GDS。讨论了GDS的关键技术：基于标识的特征表示模型，标识子系统、统一二、三维约束的基于子图的草图设计及约束求解方法、基于约束依赖图的特征编辑算法等。     

一种基于边松弛的大规模WSN分簇定位算法

针对大规模WSN定位问题中,基于半定规划的分簇定位算法在分簇不均匀及节点密度较大时,部分簇会出现定位计算复杂度过高的问题,提出了一种新的基于边松弛的分簇定位算法-EES-Cluster.该算法通过对每一个网络簇子图进行边的松弛预处理,减少了边的数目;在网络分簇数目较少时,能有效降低定位过程的计算复杂度,同时较好地保持较高的定位精度,减小簇头节点信息融合的功耗.仿真实验及分析表明,EES-Cluster算法能有效降低分簇定位算法的计算复杂度,提高大规模WSN的定位效率.     

一种密集部署传感器网络的分簇算法

针对分簇算法中的重新分簇所带来的高负载问题,提出了一种基于完全图的能量有效的分簇算法(CGCA),系统启动时刻,CGCA把网络划分成多个完全图,每个完全图独立成簇.CGCA利用完全图中节点之间是等价的性质,只是在系统启动的时刻执行分簇算法,而在以后的重新选举簇头阶段,簇头只需要在每个簇的内部节点间进行轮换,而不是像以前的分簇算法需要进行全局性的触发来选举簇头,这使得CGCA的通信和计算负载可以大量减少,它在单个节点的处理复杂度和消息复杂度均为O(1).另外,通过优先选择距离簇头近的节点加入簇内,CGCA不仅减少了簇头和簇内成员的簇内通信能量,而且使得簇头比较均匀地分布在部署区域.仿真实验表明:在节点密集部署的情况下,CGCA产生的消息交换个数远小于HEED分簇算法,最后在簇头均匀分布方面,CGCA也明显优于LEACH分簇算法.     

基于MapReduce的互联网拓扑特征参数算法研究

针对传统单机算法在计算大规模互联网拓扑特征参数时效率低的问题,基于MapReduce分布式计算框架对网络拓扑特征参数算法进行研究。通过分析单机图算法并行移植时存在的问题,提出了图算法并行化设计的原则和消息传递机制;根据设计原则和消息传递机制,为4个网络拓扑参数设计了并行算法。实验证明,并行的拓扑参数算法能够有效提高计算效率,且具备良好的可扩展性。     

一种基于分簇复制的DAG任务图调度算法

并行任务调度是影响机群计算效率的关键因素之一，机群环境DAG(Directed Acyclic Graph)任务图调度是一个NP完全问题，只能寻求启发式算法。已有的研究中，图解重构算法在允许任务复制的条件下，通过对DAG图递归分解与子图重构，初步实现了一个可行的调度方案。该文在此基础上，提出了以调度长度增量为依据的任务复制策略，利用该策略调整受制约节点的同簇前驱，解决了任务簇间的时间制约问题，缩短了调度长度；通过合理地选择任务簇进行合并，增大任务簇的粒度，提高了处理器的利用率。提出的以任务簇扩展-合并为特征、以分簇复制为手段的DAG图调度算法，改进和拓展了图解重构方法。实例分析表明本算法复杂度与TDS (Task Duplication Scheduling)相同，但性能更优。     

反馈集问题的研究进展

反馈集问题是经典的NP难问题,在电路测试、操作系统解死锁、分析工艺流程、生物计算等领域都有重要应用,按照反馈集中元素类型可分为反馈顶点集(FVS)问题和反馈边集(FAS)问题。人们利用线性规划和局部搜索等技术设计了一系列关于FVS和FAS问题的近似算法,并基于分枝一剪枝策略和加权分治技术提出了FVS问题的精确算法。随着参数计算理论的发展,近年来参数化反馈集问题引起了人们的重视,并取得了很大突破。目前已经证明了无向图和有向图中FVS问题和FAS问题都是固定参数可解的(FPT)。利用树分解、分支搜索、迭代压缩等技术,对无向图FVS问题提出了一系列FPT算法。针对某些特殊的应用,人们开展了对具有特殊性质的图上FVS问题的研究,提出了一些多项式时间可解的精确算法。现首先介绍了在无向图中关于FVS问题的近似算法与精确算法,然后具体分析了FVS问题的参数化算法。进一步阐述了关于有向图和特殊图上FVS问题的研究现状,介绍了FAS问题的研究成果。基于对反馈集问题研究现状的分析,提出了今后FVS问题研究中值得关注的几个方面。     

面向实体识别的聚类算法

实体识别是数据质量的一个重要方面,对于大数据处理不可或缺.已有的实体识别研究工作聚焦于数据对象相似度算法、分块技术和监督的实体识别技术,而非监督的实体识别中匹配决定的问题很少被涉及.提出一种面向实体识别的聚类算法来弥补这个缺失.利用数据对象及其相似度构建带权重的数据对象相似图.聚类过程中,利用相似图上重启式随机游走来动态地计算类簇与结点的相似度.聚类的基本逻辑是,类簇迭代地吸收离它最近的结点.提出数据对象排序方法来优化聚类的顺序,提高聚类精确性;提出了优化的随机游走平稳概率分布计算方法,降低聚类算法开销.通过在真实数据集和生成数据集上的对比实验,验证了该算法的有效性.     

Going weighted: Parameterized algorithms for cluster editing

The goal of the Cluster Editing problem is to make the fewest changes to the edge set of an input graph such that the resulting graph is a disjoint union of cliques. This problem is NP-complete but recently, several parameterized algorithms have been proposed. In this paper, we present a number of surprisingly simple search tree algorithms for Weighted Cluster Editing assuming that edge insertion and deletion costs are positive integers. We show that the smallest search tree has size O(1.82^k) for edit cost k, resulting in the currently fastest parameterized algorithm, both for this problem and its unweighted counterpart. We have implemented and compared our algorithms, and achieved promising results.¹     

Using Nondeterminism to Design Efficient Deterministic Algorithms

In this paper we illustrate how nondeterminism can be used conveniently and effectively in designing efficient deterministic algorithms. In particular, our method gives a parameterized algorithm of running time O((5.7 k)^k n) for the 3-D matching problem, which significantly improves the previous algorithm by Downey et al. The algorithm can be generalized to yield an improved algorithm for the r-D matching problem for any positive integer r. The method can also be employed in designing deterministic algorithms for other optimization problems as well.     

A survey of parameterized algorithms and the complexity of edge modification

The survey is a comprehensive overview of the developing area of parameterized algorithms for graph modification problems. It describes state of the art in kernelization, subexponential algorithms, and parameterized complexity of graph modification. The main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties. To facilitate further research, we list many open problems in the area.     

可满足性问题的研究综述

对SAT问题及其各种约束子问题进行分类并给出具体定义,着重介绍常规SAT问题、最大可满足性问题（MAX—SAT）和参数化SAT问题的相关算法,并对参数算法中运用的技术进行分析和比较,提出一些SAT问题研究中值得关注的几个方面。     

Subexponential algorithms for partial cover problems

Partial Cover problems are optimization versions of fundamental and well-studied problems like Vertex Cover and Dominating Set. Here one is interested in covering (or dominating) the maximum number of edges (or vertices) using a given number k of vertices, rather than covering all edges (or vertices). In general graphs, these problems are hard for parameterized complexity classes when parameterized by k. It was recently shown by Amini et al. (2008) [1] that Partial Vertex Cover and Partial Dominating Set are fixed parameter tractable on large classes of sparse graphs, namely H-minor-free graphs, which include planar graphs and graphs of bounded genus. In particular, it was shown that on planar graphs both problems can be solved in time ²O(k)nO(1).During the last decade there has been an extensive study on parameterized subexponential algorithms. In particular, it was shown that the classical Vertex Cover and Dominating Set problems can be solved in subexponential time on H-minor-free graphs. The techniques developed to obtain subexponential algorithms for classical problems do not apply to partial cover problems. It was left as an open problem by Amini et al. (2008) [1] whether there is a subexponential algorithm for Partial Vertex Cover and Partial Dominating Set. In this paper, we answer the question affirmatively by solving both problems in time not only on planar graphs but also on much larger classes of graphs, namely, apex-minor-free graphs. Compared to previously known algorithms for these problems our algorithms are significantly faster and simpler.     

The Compatibility of Binary Characters on Phylogenetic Networks: Complexity and Parameterized Algorithms

In a recent article, Nakhleh, Ringe and Warnow introduced perfect phylogenetic networks—a model of language evolution where languages do not evolve via clean speciation—and formulated a set of problems for their accurate reconstruction. Their new methodology assumes networks, rather than trees, as the correct model to capture the evolutionary history of natural languages. They proved the NP-hardness of the problem of testing whether a network is a perfect phylogenetic one for characters exhibiting at least three states, leaving open the case of binary characters, and gave a straightforward brute-force parameterized algorithm for the problem of running time O(3 ^k n), where k is the number of bidirectional edges in the network and n is its size. In this paper, we first establish the NP-hardness of the binary case of the problem. Then we provide a more efficient parameterized algorithm for this case running in time O(2 ^k n ²). The presented algorithm is very simple, and utilizes some structural results and elegant operations developed in this paper that can be useful on their own in the design of heuristic algorithms for the problem. The analysis phase of the algorithm is very elegant using amortized techniques to show that the upper bound on the running time of the algorithm is much tighter than the upper bound obtained under a conservative worst-case scenario assumption. Our results bear significant impact on reconstructing evolutionary histories of languages—particularly from phonological and morphological character data, most of which exhibit at most two states (i.e., are binary), as well as on the design and analysis of parameterized algorithms. Research of I.A. Kanj was supported in part by DePaul University Competitive Research Grant.     

Steiner Tree问题的研究进展

Steiner树问题是经典的NP难解问题,在计算机网络布局、电路设计以及生物网络等领域都有很多应用。随着参数计算理论的发展,已经证明了无向图和有向图中的Steiner树问题都是固定参数可解的(FPT)。介绍了无向图和有向图中Steiner树问题的近似算法和参数算法,分析了一些特殊Steiner树问题的研究现状,还讨论了顶点加权Steiner树问题的研究进展。最后,提出了该问题的进一步研究方向。     

Towards hybrid evolutionary algorithms

Metaheuristics have received considerable interest these recent years in the field of combinatorial optimization. However, the choice of a particular algorithm to optimize a certain problem is still mainly driven by some sort of devotion of its author to a certain technique rather than by a rationalistic choice driven by reason. Hybrid algorithms have shown their ability to provide local optima of high quality. Hybridization of algorithms is still in its infancy: certain combinations of algorithms have experimentally shown their performance, though the reasons of their success is not always really clear. In order to add some rational to these issues, we study the structure of search spaces and attempt to relate it to the performance of algorithms. We wish to explain the behavior of search algorithms with this knowledge and provide guidelines in the design of hybrid algorithms. This paper briefly reviews the current knowledge we have on search spaces of combinatorial optimization problems. Then, we discuss hybridization and present a general classification of the way hybridization can be conducted in the light of our knowledge of the structure of search spaces.     

枚举单体型组装问题多个最优解的遗传算法设计

单体型组装问题就是根据个体基因组测序获得的DNA序列数据重构出该个体的一对单体型。目前单体型组装问题的各种优化计算模型已有相关的启发式算法和参数化精确算法,但是这些算法只能得出一个最优解,即一对单体型。可是生物问题的最优解往往不是唯一的,或者真实解可能只是接近最优的。该文设计了一个新的能枚举出最优的多个解的遗传算法。实验结果表明该算法具有较高的单体型重建精度,并为生物学家根据领域知识在算法获得的多个解的基础进一步选择提供了可能。