带权区间图的最短路算法

提出一个解带权区间图的最短路问题的O(nα(n))时间新算法，其中n是带权区间图中带权区间的个数，α(n)是单变量Ackerman函数的逆函数，它是一个增长速度比log n慢得多的函数，对于通常所见到的n，α(n)≤4．本文提出的新算法不仅在时间复杂性上比直接用Dijkstra算法解带权区间图的最短路问题有较大改进，而且算法设计思想简单，易于理解和实现．     

区间值强模糊图的运算性质

利用经典图和模糊图定义和性质,给出了区间值模糊关系、模糊变换以及区间值强模糊图的定义,相应地定义了区间值强模糊图弱直积、半直积运算,并且证明了其弱直积、半直积运算封闭的性质。     

基于贪婪策略的紧密k核子图查询

k核查询是一种社团查询,由于其可以在线性时间内被有效计算,因此在社团检测中具有较广泛的应用。图中边的权值在很多场景下具有较强的语义关系,但现有研究较少考虑图中边的权值。为提升k核查询的效率,在k核的基础上定义加权图中的紧密k核子图查询（CRKSQ）问题,并使用归约方法证明该问题是NP-难的。基于贪婪策略设计启发式算法CRK-G,通过迭代删除节点为CRKSQ问题找到一个近似解。在此基础上,从降低图规模和减少迭代次数两方面研究CRK-G算法的优化策略,分别提出使用图压缩策略的算法CRK-C及使用单次多节点删除策略的算法CRK-F。在Bio-GRID、Email-Enron、DBLP 3个数据集上的实验结果表明,相对于CRK-G算法,CRK-C、CRK-F算法在查询速度上有较大的提升,且平均误差均在8%以内。     

可变抽样区间二元双抽样广义方差控制图

将可变抽样区间特性融入二元双抽样广义方差控制图,构建可变抽样区间二元双抽样广义方差控制图及其监控方法.采用马尔科夫链方法完成控制图调整的平均报警时间和平均报警时间性能指标的计算,进而建立用控制图参数设计的优化模型,并通过遗传算法完成模型求解.通过与可变抽样区间的二元广义方差合成控制图、二元双抽样广义方差控制图以及基于Cornish-Fisher修正的二元双抽样广义方差控制图的判异性能对比,验证该控制图的优势,并通过加工实例对性能优势进行进一步说明.     

带区间参数的影响图

对传统影响图进行了扩充,提出了带区间参数的影响图(ID)概念,在此基础上,给出了基于遗传算法(GA)的带区间参数影响图的结构学习方法,采用Gibbs采样算法对该类影响图作了近似推理,并应用于具体实例.实验表明,带区间参数的影响图模型适用于求解模糊事件和值不确定事件的概率.     

图数据流上时间尊重图模式匹配算法研究

现有的动态子图匹配研究中忽略了模式图中的时间信息,使用户难以得到想要查询的真实结果.针对这种情况,首先设计一种简洁的中间结果保存形式,将匹配结果直接在数据图中以图进行存储;接着改进边缘转换模型,当数据图有边插入/删除时对其快速增量维护并报告结果;最后根据边转换模型设计了一个时间尊重图模式匹配算法,提高了匹配搜索效率.对真实网络流量数据和综合社交流数据进行实验评估,结果表明算法能够有效减少图模式匹配的执行时间和空间花销.     

团图点删除问题的近似算法

针对团图点删除问题的3-近似算法得到的近似解可能较大的问题,通过对团图点删除问题及团图特性的分析,提出了该问题的一个新的近似算法。新算法通过考察图中节点的一阶和二阶邻点来计算节点关联的P3的数目,然后优先选择P3数最大的节点加入解集,以期尽快消除图中的P3,从而最终获得较小的点删除集。为检验算法效果,设计了多组不同场景的随机实验对新算法和经典的3-近似算法进行了比较。随机实验表明,新算法较经典的3-近似算法有明显的优势。     

求解区间图上的罗马控制数的动态规划算法

摘 要: 针对区间图的最小罗马控制函数和罗马控制数求解的困难性,本文提出了一个动态规划算法。从区间图的顶点排序开始,结合区间图的某些性质,采用逐步搜索的方法,不断扩大搜索的顶点集合范围,最终求出最优的罗马控制集和罗马控制数。为保证算法的正确性和科学性,对算法进行了严格的数学推理和证明。最后还给出了一个典型的区间图求解过程的演示示例,增强了算法的可读性和可操作性。结果表明该算法不仅运算速度快,而且简单易行。 关键词: 区间图;罗马控制函数;罗马控制数;权重;动态规划算法     

概率图上的对象相似度计算

在图挖掘领域,对象之间的相似度作为一个非常重要的课题,被广泛应用于链接预测、欺诈检测、协同过滤、近邻查询等众多实际问题中.在传统确定图上,节点相似度的研究受到了广泛关注并取得了很多成果.但是确定图上的对象相似度的计算无法直接应用于概率图.研究概率图上的节点相似度计算问题,定义了概率图上的期望SimRank相似度,提出了...     

计算机视觉中图匹配研究进展: 从二图匹配迈向多图匹配

图匹配试图求解二图或多图之间节点的对应关系.在图像图形领域,图匹配是一个历久弥新的基础性问题.从优化的角度来看,图匹配问题是一个组合优化问题,且在一般情形下具有非确定性多项式复杂程度(non-deter-ministic polynomial, NP)难度的性质.在过去数十年间,出现了大量求解二图匹配的近似算法,并在各个领域得到了较为广泛的应用.然而,受限于优化问题本身的理论困难和实际应用中数据质量的种种限制,各二图匹配算法在匹配精度上的性能日益趋近饱和.相比之下,由于引入了更多信息且往往更符合实际问题的设定,多图的协同匹配则逐渐成为了一个新兴且重要的研究方向.本文首先介绍了经典的二图匹配方法,随后着重介绍近年来多图匹配方法的最新进展和相关工作.最后,本文讨论了图匹配未来的发展.     

Reconstruction of interval graphs

The graph reconstruction conjecture is a long-standing open problem in graph theory. There are many algorithmic studies related to it, such as DECK CHECKING, LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING. We study these algorithmic problems by limiting the graph class to interval graphs. Since we can solve GRAPH ISOMORPHISM for interval graphs in polynomial time, DECK CHECKING for interval graphs is easily done in polynomial time. Since the number of interval graphs that can be obtained from an interval graph by adding a vertex and edges incident to it can be exponentially large, developing polynomial time algorithms for LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING on interval graphs is not trivial. We present that these three problems are solvable in polynomial time on interval graphs.     

一种新的高效图聚集算法

图聚集是将一个大规模的图用简洁的并能有效反映原始图的结构和属性信息的小规模图来表示的技术.图聚集在图数据管理、分析和可视化中发挥着重要作用.图聚集方面现有研究结果还很少,也很不系统.其主要不足之处是:1)算法依赖于具体应用;2)算法仅考虑了图的某方面信息,如结构信息或属性信息;3)算法对用户提供的交互和反馈信息的约束很强.针对现有图聚集算法存在的主要不足,提出一种有向图新型图聚集算法,该算法采用一种新的聚集图质量函数,全面刻画了聚集图多样性、覆盖性、简洁性和实用性.该算法使用LSH(locality sensitive Hashing)技术和基于熵的划分技术,保证了聚集图的质量.在真实数据集上进行了大量的实验,验证了算法的有效性.     

超网络能量研究与应用

图能量是图论研究的重要内容,图能量及其变种已在无向图、有向图、混合图等其他多种类型的图中得到很多成功的应用.超网络是一类较传统意义上的复杂网络更为复杂的网络.大多数图能量均是基于矩阵特征值计算得到的,无法推广应用到超网络中,应用范围受限.基于网络维数的网络能量已先后应用于无向图、有向图等多种类型图的分析研究中,并与无向...     

Tree spanners on chordal graphs: complexity and algorithms

A tree t-spanner T in a graph G is a spanning tree of G such that the distance in T between every pair of vertices is at most t times their distance in G. The T t-S problem asks whether a graph admits a tree t-spanner, given t. We substantially strengthen the hardness result of Cai and Corneil (SIAM J. Discrete Math. 8 (1995) 359–387) by showing that, for any t4, T t-S is NP-complete even on chordal graphs of diameter at most t+1 (if t is even), respectively, at most t+2 (if t is odd). Then we point out that every chordal graph of diameter at most t−1 (respectively, t−2) admits a tree t-spanner whenever t2 is even (respectively, t3 is odd), and such a tree spanner can be constructed in linear time.

The complexity status of T 3-S still remains open for chordal graphs, even on the subclass of undirected path graphs that are strongly chordal as well. For other important subclasses of chordal graphs, such as very strongly chordal graphs (containing all interval graphs), 1-split graphs (containing all split graphs) and chordal graphs of diameter at most 2, we are able to decide T 3-S efficiently.     

k-tuple domination in graphs

In a graph G, a vertex is said to dominate itself and all of its neighbors. For a fixed positive integer k, the k-tuple domination problem is to find a minimum sized vertex subset in a graph such that every vertex in the graph is dominated by at least k vertices in this set. The current paper studies k-tuple domination in graphs from an algorithmic point of view. In particular, we give a linear-time algorithm for the k-tuple domination problem in strongly chordal graphs, which is a subclass of chordal graphs and includes trees, block graphs, interval graphs and directed path graphs. We also prove that the k-tuple domination problem is NP-complete for split graphs (a subclass of chordal graphs) and for bipartite graphs.     

大规模图处理研究

大数据研究领域的许多问题可以转换为图的问题。本文将阐述鲲鹏大数据系统计算引擎中有关大规模图处理的研究进展以及应用,具体包括高效子图匹配算法、面向图的稀疏数据存储结构和大规模图异步计算模型及其在基因拼接中的应用。     

Polynomial-time algorithms for weighted efficient domination problems in AT-free graphs and dually chordal graphs

An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph. The minimum weight efficient domination problem is the problem of finding an efficient dominating set of minimum weight in a given vertex-weighted graph; the maximum weight efficient domination problem is defined similarly. We develop a framework for solving the weighted efficient domination problems based on a reduction to the maximum weight independent set problem in the square of the input graph. Using this approach, we improve on several previous results from the literature by deriving polynomial-time algorithms for the weighted efficient domination problems in the classes of dually chordal and AT-free graphs. In particular, this answers a question by Lu and Tang regarding the complexity of the minimum weight efficient domination problem in strongly chordal graphs.     

嵌入一致图语法的依赖图

图语法将字符串上的形式文法扩充为图上的形式文法,提供一种能够使用精确的数学方法来模拟图变换的机制.提出了几种新的基于一致图语法的方法来表示控制流图、数据流图、控制数据流图、二分图和超图,并说明如何通过图重写来自动生成依赖图并挖掘并行性,从而协助并行编译器和并行语言的设计和实现.     

软件图语言的形式描述

本文从语言学和形式化角度对软件领域中广泛使用的软件图进行了研究，提出了软件图语言这一概念。本文首先提出了关于软件图语言的一组基本概念，其次研究软件图语言的同态和同构，以构成软件图形式描述的基础；最后讨论了软件图语言的形式表示法，并提出了基于图符网的文法，使图文法更适合于表示软件图语言。本文工作可以作为设计面向软件图语言的软件工具的基础。     

Digraph decompositions and monotonicity in digraph searching

Graph decompositions such as tree-decompositions and associated width measures have been the focus of much attention in structural and algorithmic graph theory. In particular, it has been found that many otherwise intractable problems become tractable on graph classes of bounded tree-width.More recently, proposals have been made to define a similar notion to tree-width for directed graphs. Several proposals have appeared so far, supported by algorithmic applications.In this paper we explore the limits of algorithmic applicability of digraph decompositions and show that various natural candidates for problems, which potentially could benefit from digraphs having small “directed width”, remain NP-complete even on almost acyclic graphs.Closely related to graph and digraph decompositions are graph searching games. An important property of graph searching games is monotonicity and a large number of papers addresses the question whether particular variants of these games are monotone. However, so far for two natural types of graph searching games-underlying DAG- and Kelly-decompositions-the question whether they are monotone was still open.We settle this issue by showing that both variants, the visible and the inert invisible graph searching games on directed graphs, are non-monotone.