限制树宽的图的最小标记生成数算法

本文研究了图的最小标记生成树问题。首先介绍在一般图上基于搜索树的最小标记生成树的算法;然后考虑了限制树宽的图,得到了效率更高的算法。该算法在树宽为常数的情况下,时间复杂度关于图的顶点个数为多项式,从而也证明了最小标记生成树在限制树宽的图上属于确定参数可解问题。     

基于Dandelion编码生成有界树宽CP-nets

针对条件偏好网络（CP-nets）图模型在进行推理运算时的高时间复杂度的问题,提出了一种基于Dandelion编码生成有界树宽的CP-nets（BTW-CP-nets Gen）算法。首先,通过Dandelion编码与树宽为k的树结构（k-tree）之间的双向映射原理推导出Dandelion编码与k-tree之间的解码与编码算法,实现编码与树结构的一对一映射;其次,利用k-tree来约束CP-nets结构的树宽,并利用k-tree的特征树得到了CP-nets的有向无环图结构;最后,利用离散多值函数的双射计算出各CP-nets结构节点的条件偏好表,然后针对生成的有界树宽CP-nets进行占优查询检测。理论分析和实验数据表明,与Pruffer编码生成k-tree（Pruffer code）算法相比,BTW-CP-nets Gen算法的运行时间在生成简单结构和复杂结构时的下降幅度分别为21.1%和30.5%;而BTW-CP-nets Gen算法所生成的图模型在进行占优查询时的节点遍历比在简单结构和复杂结构上分别提高了18.48%和29.03%。BTW-CP-nets Gen算法在更短的时间内,占优查询时遍历的节点率更高。可见,BTW-CP-nets Gen算法在图模型的推理中能够有效提高算法效率。     

基于图的多视角聚类算法综述

多视角聚类通过利用多视角之间的互补性和一致性信息来提高聚类的性能.近年来受到越来越多的关注.为了及时掌握目前基于图的多视角聚类算法的研究现状与最新技术,对大量的、最新的多视角图聚类进行调查、归纳整理、分类及总结.根据多视角聚类涉及的算法机制和数学原理,并进一步分为基于图、基于网络和基于谱的聚类方法.不仅详细介绍了每一类...     

基于节点聚类复杂度的图聚类方法

图聚类可以发现网络中的社区结构,是复杂网络分析中的一项重要任务。针对不同节点的聚类难度各异的问题,提出了一种基于节点聚类复杂度的图聚类算法(Graph Clustering Algorithm Based on Node Clustering Complexity, GCNCC),用于判断节点的聚类复杂度,为聚类复杂度低的节点赋予伪标签,利用伪标签提供的监督信息降低其他节点的聚类复杂度,进而得到网络聚类结果。GCNCC包括节点表示、节点聚类复杂度判别和图聚类3个主要模块。节点表示模块得到保持网络集聚性的表示;节点聚类复杂度判别模块用于判断网络中的低聚类复杂度节点,并利用低聚类复杂度节点的伪标签信息来优化更新网络中其他节点的聚类复杂度;图聚类模块采用标签传播方法,将低聚类复杂度节点标签传播给高聚类复杂度节点,以得到聚类结果。在3个真实的引文网络和3个生物数据集上与9种经典算法进行对比,算法GCNCC在ACC,NMI,ARI和F1等方面均表现良好。     

图聚类算法的评价模型

关系数据可抽象为网络,在通常情况下,缺乏对这些现实网络背景知识的了解。为了评价图聚类算法在现实网络上的性能表现,构建了一种接近现实的网络模型,通过算法在模型网络上的性能表现来推断其分析现实网络的能力。为了确保此推断的合理性,构建的模型网络具有与所研究网络完全相同的一阶统计特征。同时,构建的模型网络可具有任意设定的集团结构,这就相当于给定了背景知识,即真实的分类信息是已知的。实例说明,构建的模型为客观评价图聚类算法提供了一条途径。     

基于图聚类与蚁群算法的社交网络聚类算法

针对社交网络中社交关系的有向性与多样性,提出了一种基于图聚类与蚁群算法的社交网络聚类算法。首先,在网络覆盖率的约束下为社交网络建立有向、非全连接的二维图模型;然后,采用K-medoids算法搜索用户分组的中心用户,采用人工蚁群算法在2D图中搜索各个用户与中心用户的相似性,将满足相似性阈值的用户分为同一个用户组。设计了低活跃用户的预测机制解决网络的稀疏性问题与冷启动问题。此外,通过网络覆盖率的约束条件权衡聚类准确率与覆盖率两个指标。仿真实验结果表明,该算法实现了较好的社交网络聚类性能,并且有效地缓解了稀疏性问题与冷启动问题。     

一种数据挖掘中的W-PAM限制聚类算法

在数据挖掘中由于每个数据对象对于知识发现的作用是不同的,为了区分这些相异之处,给每个对象赋予一定量的值,因此在PAM聚类算法的基础上提出一种W-PAM(Weight Partitioning Around Medoids)聚类算法,它为簇中数据对象加入权重来提高算法的准确率,此外利用数据对象间的关联限制能够提高聚类算法的效果。探讨了一种W-PAM算法与关联限制相结合的限制聚类算法,该算法同时拥有W-PAM算法和关联限制的优点。实验结果证明,W-PAM的限制聚类算法可以更有效地利用所给的关联限制来改善聚类效果,提高算法的准确率。     

基于图神经网络的聚类研究

近年来,深度学习在人工智能、计算机视觉等各个领域都有突出表现,成为越来越多学者关注的热点.目前,一般的神经网络只能够解决欧式空间数据,对于社交网络、推荐系统等非欧式空间数据,就需要结合图论的相关知识来分析隐藏的结构信息.因此引入图神经网络的概念,对一般的深度聚类进行改进,目的 是在处理高维复杂数据的同时,还尽可能地保留原始的数据结构信息,实现优化聚类的目标.     

基于核心图聚类的邮件网络社区发现

根据图聚类节点的密度变化确定核心节点,构成连通子图并确定邮件网络社区划分的个数及初始社区中心点,通过社区中心动态调整的方法将非核心节点划分至所属社区.实验证明了该邮件网络社区划分的有效性和可行性.     

基于DNA计算的层次图聚类算法

为解决使用DNA计算图聚类问题,提出一种基于DNA计算的层次图聚类算法。在分裂层次聚类中,使用DNA分子对图中顶点、边进行编码,在试管中并行产生最小生成树,根据给定阈值,通过切割树枝得到聚类结果。在凝聚聚类中使用DNA计算产生哈密尔顿路径,通过寻找最短哈密尔顿路径得到聚类结果。实验结果验证了该算法的可行性。     

Property Testing in Bounded Degree Graphs

Abstract. We further develop the study of testing graph properties as initiated by Goldreich, Goldwasser and Ron. Loosely speaking, given an oracle access to a graph, we wish to distinguish the case when the graph has a pre-determined property from the case when it is ``far' from having this property. Whereas they view graphs as represented by their adjacency matrix and measure the distance between graphs as a fraction of all possible vertex pairs, we view graphs as represented by bounded-length incidence lists and measure the distance between graphs as a fraction of the maximum possible number of edges. Thus, while the previous model is most appropriate for the study of dense graphs, our model is most appropriate for the study of bounded-degree graphs. In particular, we present randomized algorithms for testing whether an unknown bounded-degree graph is connected, k -connected (for k>1 ), cycle-free and Eulerian. Our algorithms work in time polynomial in 1/ɛ , always accept the graph when it has the tested property, and reject with high probability if the graph is ɛ -far from having the property. For example, the 2-connectivity algorithm rejects (with high probability) any N -vertex d -degree graph for which more than ɛ dN edges need to be added in order to make the graph 2-edge-connected. In addition we prove lower bounds of Ω(\sqrt N ) on the query complexity of testing algorithms for the bipartite and expander properties.     

I/O-Efficient Algorithms for Graphs of Bounded Treewidth

We present an algorithm that takes I/Os (sort(N)=Θ((N/(DB))log  _M/B (N/B)) is the number of I/Os it takes to sort N data items) to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N, where k is a constant. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in I/Os, including the single-source shortest path problem and a number of problems that are NP-hard on general graphs. The tree decomposition can also be used to obtain an optimal separator decomposition of G. We use such a decomposition to perform depth-first search in G in  I/Os. As important tools that are used in the tree decomposition algorithm, we introduce flippable DAGs and present an algorithm that computes a perfect elimination ordering of a k-tree in I/Os. The second contribution of our paper, which is of independent interest, is a general and simple framework for obtaining I/O-efficient algorithms for a number of graph problems that can be solved using greedy algorithms in internal memory. We apply this framework in order to obtain an improved algorithm for finding a maximal matching and the first deterministic I/O-efficient algorithm for finding a maximal independent set of an arbitrary graph. Both algorithms take I/Os. The maximal matching algorithm is used in the tree decomposition algorithm. An abstract of this paper was presented at the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, Proceedings, pp. 89–90, 2001. Research of A. Maheshwari supported by NSERC. Part of this work was done while the second author was a Ph.D. student at the School of Computer Science of Carleton University.     

Resource Allocation in Bounded Degree Trees

We study the bandwidth allocation problem (bap) in bounded degree trees. In this problem we are given a tree and a set of connection requests. Each request consists of a path in the tree, a bandwidth requirement, and a weight. Our goal is to find a maximum weight subset S of requests such that, for every edge e, the total bandwidth of requests in S whose path contains e is at most 1. We also consider the storage allocation problem (sap), in which it is also required that every request in the solution is given the same contiguous portion of the resource in every edge in its path. We present a deterministic approximation algorithm for bap in bounded degree trees with ratio . Our algorithm is based on a novel application of the local ratio technique in which the available bandwidth is divided into narrow strips and requests with very small bandwidths are allocated in these strips. We also present a randomized (2+ε)-approximation algorithm for bap in bounded degree trees. The best previously known ratio for bap in general trees is 5. We present a reduction from sap to bap that works for instances where the tree is a line and the bandwidths are very small. It follows that there exists a deterministic 2.582-approximation algorithm and a randomized (2+ε)-approximation algorithm for sap in the line. The best previously known ratio for this problem is 7. A preliminary version of this paper was presented at the 14th Annual European Symposium on Algorithms (ESA), 2006.     

Exact and Approximation Algorithms for Clustering

In this paper we present an n^ O(k ^1-1/d ) -time algorithm for solving the k -center problem in \reals ^d , under L _∈ fty - and L ₂ -metrics. The algorithm extends to other metrics, and to the discrete k -center problem. We also describe a simple (1+ɛ) -approximation algorithm for the k -center problem, with running time O(nlog k) + (k/ɛ)^ O(k ^1-1/d ) . Finally, we present an n^ O(k ^1-1/d ) -time algorithm for solving the L -capacitated k -center problem, provided that L=Ω(n/k ^1-1/d ) or L=O(1) . Received July 25, 2000; revised April 6, 2001.     

On the Sum Coloring Problem on Interval Graphs

In this paper we study the following NP-complete problem: given an interval graph G = (V,E) , find a node p -coloring such that the cost is minimal, where denotes a partition of V whose subsets are ordered by nonincreasing cardinality. We present an O(m χ (G) + n log n) time ε -approximate algorithm (ε < 2) to solve the problem, where n , m , and χ #(G) are the number of nodes of the interval graph, its number of cliques, and its chromatic number, respectively. The algorithm is shown to solve the problem exactly on some classes of interval graphs, namely, the proper and the containment interval graphs, and the intersection graphs of sets of ``short' intervals. The problem of determining the minimum number of colors needed to achieve the minimum over all p -colorings of G is also addressed. Received February 1, 1996; revised August 22, 1997.     

Diameter and Treewidth in Minor-Closed Graph Families,Revisited

Eppstein [5] characterized the minor-closed graph families for which the treewidth is bounded by a function of the diameter, which includes, e.g., planar graphs. This characterization has been used as the basis for several (approximation) algorithms on such graphs (e.g., [2] and [5]–[8]). The proof of Eppstein is complicated. In this short paper we obtain the same characterization with a simple proof. In addition, the relation between treewidth and diameter is slightly better and explicit.     

Dynamically Switching Vertices in Planar Graphs

We consider graphs whose vertices may be in one of two different states: either on or off . We wish to maintain dynamically such graphs under an intermixed sequence of updates and queries. An update may reverse the status of a vertex, by switching it either on or off , and may insert a new edge or delete an existing edge. A query tests whether any two given vertices are connected in the subgraph induced by the vertices that are on . We give efficient algorithms that maintain information about connectivity on planar graphs in O( log ³ n) amortized time per query, insert, delete, switch-on, and switch-off operation over sequences of at least Ω(n) operations, where n is the number of vertices of the graph. Received September 1997; revised January 1999.     

Constructing Plane Spanners of Bounded Degree and Low Weight

Given a set S of n points in the plane, we give an O(n log n)-time algorithm that constructs a plane t-spanner for S, with t ≈ 10, such that the degree of each point of S is bounded from above by 27, and the total edge length is proportional to the weight of a minimum spanning tree of S. Previously, no algorithms were known for constructing plane t-spanners of bounded degree.     

基于广义关联聚类图的分层关联多目标跟踪

检测跟踪是近期多目标跟踪研究的热点方向之一.目前大部分方法都是基于相邻帧之间的双向匹配,对检测点进行数据融合.本文提出的方法是,给定一个滑动时间窗口,在窗口内对某个目标每帧出现的检测点进行一次性数据融合.我们把多目标跟踪看作图的分割问题,利用广义关联聚类（Generalized correlation clustering problem,GCCP）图优化文中提出的数据融合.吸取分层数据关联的思想,把多目标跟踪分成两个阶段.首先,在时间窗口内遵循检测点,利用广义关联聚类,得到自适应长度的轨迹片段,轨迹片段长度不受窗口宽度的限制.然后,基于轨迹片段进一步数据关联,得到目标的长轨迹.在公共数据集上的实验测试表明,本文方法能够有效地实现多目标跟踪,对于遮挡处理、身份转换处理以及轨迹的生成具有很好的鲁棒性,多目标跟踪准确率（Multiple object tracking accuracy,MOTA）超过当前水平.