Computing All Pairs Shortest Paths on Sparse Graphs with Articulation Points

In most network analysis tools the computation of the shortest paths between all pairs of nodes is a fundamental step to the discovery of other properties. Among other properties is the computation of closeness centrality, a measure of the nodes that shows how central a vertex is on a given network. In this paper, the authors present a method to compute the All Pairs Shortest Paths on graphs that present two characteristics： abundance of nodes with degree value one, and existence of articulation points along the graph. These characteristics are present in many real life networks especially in networks that show a power law degree distribution as is the case of biological networks. The authors＇ method compacts the single nodes to their source, and then by using the network articulation points it disconnects the network and computes the shortest paths in the biconnected components. At the final step the authors proposed methods merges the results to provide the whole network shortest paths. The authors＇ method achieves remarkable speedup compared to state of the art methods to compute the shortest paths, as much as 7 fold speed up in artificial graphs and 3.25 fold speed up in real application graphs. The authors＇ performance improvement is unlike previous research as it does not involve elaborated setups since the authors algorithm can process significant instances on a popular workstation.

Improving Centralized Path Calculation Based on Graph Compression

Shortest-path calculation on weighted graphs are an essential operation in computer networks. The performance of such algorithms has become a critical challenge in emerging software-defined networks(SDN),since SDN controllers need to centralizedly perform a shortest-path query for every flow,usually on large-scale network. Unfortunately,one of the challenges is that current algorithms will become incalculable as the network size increases. Therefore, inspired by the compression graph in the field of compute visualization,we propose an efficient shortest path algorithm by compressing the original big network graph into a small one, but the important graph properties used to calculate path is reserved. We implement a centralized version of our approach in SDN-enabled network,and the evaluations validate the improvement compared with the well-known algorithms.

基于树分解的时序最短路径计数查询算法

最短路径计数是图计算中的一个重要研究问题,旨在查询顶点间的最短路径数,在路径规划与推荐、社交网络分析、介数中心性计算等领域中具有广泛应用。目前越来越多的网络可以建模为时序图,但少有针对时序图最短路径计数查询问题的研究工作。与静态图相比,时序图增加了时间信息,结构更复杂,在查询顶点间的路径数时必须考虑边的激活时间,因此静态图中最短路径计数方法不再适用于时序图,并且在大规模时序图上查询更具有挑战性。针对时序图最短路径计数问题,提出一种基于树分解构建TG-TL(Temporal Graph-Tree Label)索引的方法。该方法包含构建索引和在线查询两个阶段,构建索引阶段根据时序图的属性设计时序树分解算法,将时序图转化为树结构;然后根据树分解的结构信息以及凸路径定义提出高效构建索引算法;在线查询阶段基于TG-TL索引提出了高效的时序最短路径计数查询算法。在4个真实数据集上的实验结果表明,与基于TG-base(Temporal Graph-base)索引的查询算法相比,所提算法在查询效率上至少提升了61%,因此所提算法在时序图最短路径计数问题上具有高效性和有效性。

正确性可验证的密文图数据最短路径外包计算方案

地理位置、社交网络等海量图数据应用广泛且包含大量隐私,通常需要安全的外包计算来提供多样化的查询服务。然而,如何设计正确性可验证的图数据外包计算协议仍是公开的难题。为此,提出了加密图数据上正确性可验证的精确最短路径外包计算方案。该方案利用加法同态加密构造密态图数据上的广度优先最短路径计算算法,支持加密图数据的精确最短距离查询外包计算;其次,基于双线性映射累加器构造最短路径外包计算结果的概率正确性验证机制。分析和证明表明,该方案能以概率可靠性实现正确性可验证的精确最短路径的外包计算,具备随机预言模型下的IND-CCA2安全。对比实验结果表明,所提方案相比其他相关方案在安全性、功能性方面有显著优势,性能上较已有可验证图数据外包计算方案在初始化及加密环节、查询环节、验证及解密环节的时间开销分别降低了0.15%~23.19%,12.91%~30.89%和1.13%~18.62%。

结构化加密图的最短路径查询

随着云计算的快速发展,数据用户将大量图数据外包给云以节约存储和管理成本。然而,外包数据的安全隐私问题是云计算面临的一大挑战。由于云是半诚实的,为保护敏感信息的隐私安全,数据拥有者希望在将图数据外包给云服务器之前对其加密,同时保留对加密的图数据进行查询和处理的能力。最短路径查询查找图中给定两节点之间的最短路径,是图应用中最基础的查询类型之一。目前已有许多研究者提出一系列高效的方案,以支持加密图上近似或精确最短距离查询、约束最短距离查询和top-k最近关键字查询,但支持最短路径查询的方案较少,且已有方案的存储与时间开销较大。本文提出一种支持在加密图上进行两节点间最短路径查询的结构化加密图方案。在本方案中,我们基于2-Hop标签技术构造支持有向图上最短路径查询的标签索引并加密,然后将加密的标签外包给云服务器。利用改进的保序编码算法编码距离值,实现加法运算和值的比较,提高最短路径查询的效率。在查询阶段,通过递归式地计算两节点间最短路径上的第一条边和最后一条边,最终输出完整的最短路径。安全性和性能分析证明本文方案是安全有效的,能以较小的存储和较高的查询效率实现两节点间的最短路径查询并保护图数据的隐私。

融合物品转换关系和时序信息的会话推荐算法

针对现有图神经网络会话推荐算法忽略了各类辅助信息,导致不能准确地建模会话序列的问题,提出了一种融合物品的转换关系和时序信息的会话推荐算法(RTSR)。首先利用图网络结构得到任意两个节点之间的最短路径序列,经过双向门控循环单元(GRU)将其编码为对应物品之间的转换关系,再结合自注意力机制从图的角度捕捉会话的全局依赖信息。同时设计了一种无损图编码方案来缓解会话图编码过程中信息损失的问题。该方案将会话序列中的时序信息进行合理的量化,并将其作为会话图中边的权重,再结合门控图神经网络获取会话的局部依赖信息。最后,线性组合全局依赖信息和局部依赖信息并结合反向位置信息,最终生成用户对物品的兴趣偏好,并给出推荐列表。在公共基准数据集Gowalla和Diginetica上与SR-GNN、GC-SAN、GCE-GNN等主流模型进行性能对比实验,结果表明RTSR在平均倒数排名方面分别至少提高了6.13%和1.58%,同时推荐精准度方面也有相应的提高。

Spark-GraphX框架下的大规模加权图最短路径查询

最短路径问题一直是计算机等学科的热点研究问题,常应用于社交网、交通网等诸多领域.图规模爆炸式的增长导致传统单机环境下的存储、查询已无法满足大规模图的处理需求.提出一种基于Spark-Graph X平台的大规模图最短路径查询方法(LSGSP-SG):首先利用经典算法对大规模图进行分割并标记,将割点的信息记录在文本文件中,然后利用大数据平台Spark的Graph X框架进行迭代式分布计算并进行各个计算机节点的消息通信及同步,最后返回最短路径查询结果.

Extended Lorenz majorization and frequencies of distances in an undirected network

Purpose:To contribute to the study of networks and graphs.Design/methodology/approach:We apply standard mathematical thinking.Findings:We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain.As a consequence,the average and median distances in any such network are smaller than or equal to those of a chain.Research limitations:We restricted our investigations to undirected,unweighted networks.Practical implications:We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.Originality/value:To the best of our knowledge our research contains new network results,especially those related to frequencies of distances.

含负权有向图最短路问题的新解法

通过简要分析现有含负权有向图最短路问题求解方法,基于Dijkstra算法图表法的基本原理,提出了一种新的较为直观的图表求解方法。该方法根据问题抽象所得的含负权有向图,通过确定权数来求解最短路问题,并给出了计算实例。结果表明,该方法具有实用性,且所提算法具有简便直观,计算量较少,不易出错,效率较高的特点。

基于图注意力的烟草零售店监管路线优化研究

由于城市烟草零售店较为密集,传统路径规划算法求解最优监管路径将耗费大量的运算时间,在规定时间内无法保证运算效果。并且,现有方法较少考虑求解问题的网络特性及候选子集的可解释性。鉴于此,提出一种基于图注意力的节点选择及路径优化算法(GA-SGPO),迭代选择最优坐标节点子集,在子集上进行求解以减少计算时间。此外,通过计算节点间的结构相似性,降低子集样本稀疏性。实验数据包括东莞市4万家零售店的地理坐标。实验结果显示,所提出的GA-SGPO模型在保证求解精度的同时,求解时间平均提升48%。GA-SGPO算法可显著节省计算时间,更贴近实际应用场景。而注意力机制和节点相似度计算,可为最优节点选择提供可视化依据。

Application of rough graph in relationship mining

Based on the definition of class shortest path in weighted rough graph, class shortest path algorithm in weighted rough graph is presented, which extends classical shortest path algorithm. The application in relationship mining shows effectiveness of it.

Energy Efficient Path Determination in Wireless Sensor Network Using BFS Approach

The wireless sensor networks (WSN) are formed by a large number of sensor nodes working together to provide a specific duty. However, the low energy capacity assigned to each node prompts users to look at an important design challenge such as lifetime maximization. Therefore, designing effective routing techniques that conserve scarce energy resources is a critical issue in WSN. Though, the chain-based routing is one of significant routing mechanisms but several common flaws, such as data propagation delay and redundant transmission, are associated with it. In this paper, we will be proposing an energy efficient technique based on graph theory that can be used to find out minimum path based on some defined conditions from a source node to the destination node. Initially, a sensor area is divided into number of levels by a base station based on signal strength. It is important to note that this technique will always found out minimum path and even alternate path are also saved in case of node failure.

一种基于Dijkstra的物流配送路径优化算法设计

在物流配送过程中,物流配送路径的选择是决定快递时效的关键因素。针对传统Dijkstra算法在大规模数据求解过程中效率低、耗时长的问题,文中对其进行了深入的改进和优化。在算法运行过程中,通过使用多标号模型对遍历过程进行了优化。同时,在运算过程中采用并行求解的模式来提升模型处理速度。实验测试结果表明,文中设计的路径优化算法相比传统Dijkstra算法,大规模数据的求解时间缩减了50%以上,算法并行加速比在大规模数据求解时达到了1.75倍,证明了所提算法的并行求解效率较高,具有良好的工程应用价值。

A Dynamic Programming Approach for the Max-Min Cycle Packing Problem in Even Graphs

Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles Ciin G such that s is maximum. In general, the maximum cycle packing problem is NP-hard. In this paper, it is shown for even graphs that if such a collection satisfies the condition that it minimizes the quantityon the set of all edge-disjoint cycle collections, then it is a maximum cycle packing. The paper shows that the determination of such a packing can be solved by a dynamic programming approach. For its solution, an-shortest path procedure on an appropriate acyclic networkis presented. It uses a particular monotonous node potential.

五阶递进的最短路径问题教学模式探索

最短路径问题是计算机科学、地理信息科学、运筹学、管理科学、交通工程、工业工程和复杂系统科学等领域的基础性问题,也是许多相关课程中的教学重点。针对目前教学中存在的被动接受、手工计算、只算不用等问题,按照“精选算法、纵向到底、横向到边”的教学理念,探索“算法原理—数学建模—应用举例—程序实现—算法比赛”五阶递进的最短路径问题教学模式,有助于培养和提升学生的原理掌握深度、优雅学术品位、运筹优化思维、综合应用能力和团队合作精神。

基于复杂网络的风速预测新方法

为了更准确地预测风速,首先利用可见图将风速时间序列映射到有向加权网络中,通过计算邻居时间节点的相似度并结合最短路径的方法确定网络中节点的相似度矩阵。然后在有向加权网络节点相似度分析的基础上结合相邻预测法及线性逼近法进行预测。在预测实验中,通过和其他模型的误差比较证明其适用性和可预测性,说明该方法能更准确地预测风速,可为电力系统的运行提供借鉴作用。

TD-H2H:时序图上的最短路径查询

道路网络上的最短路径查询是一个已经被广泛研究的基本问题。现有的研究通常将道路网络建模为静态图,查询给定节点间距离最短的路径。然而,道路网络具有时序性,将道路网络建模为时序图更符合实际情况。与静态图相比,时序图的规模更大,结构也更为复杂,增加了时序最短路径的查询难度。时序最短路径是指在给定出发时间下,时序图上源节点和目的节点之间旅行时间最短的路径。因此,时序最短路径的结果受给定出发时间影响,为时序最短路径的查询带来了新的挑战,传统的最短路径算法不适用于时序最短路径的查询。将道路网络建模为时序图,并基于树分解提出了TD-H2H索引,利用该索引可以快速准确地实现时序最短路经查询。首先,研究了时序图上的树分解问题,提出时序树分解算法,将图结构转变为树结构。然后,通过树分解快速确定索引结构,提出了高效的索引构建算法,用以构建TD-H2H索引。最后,基于TD-H2H设计了高效的最短路径查询算法TD-OAI。在4个真实公开的数据集上与现有算法进行了实验,结果表明提出算法的查询效率优于现有算法1~2个数量级,证明了提出算法的有效性和效率。

基于分层图的最短路径选择问题研究

路径选择问题是图论中的经典问题之一,为解决在特定约束条件下路径选择问题最短路的求取,文章采用了分层图的思想来对路径选择问题进行建模,将原图拓展为多个连接情况相同的图层,提出了一种基于分层图的最短路算法,并分别从算法思想、算法执行过程、时间复杂度等方面与传统求解方法进行比较。实验结果表明分层图最短路算法具有较低的时间复杂度与较好的性能。

Threshold-Based Shortest Path Query over Large Correlated Uncertain Graphs

With the popularity of uncertain data, queries over uncertain graphs have become a hot topic in the database community. As one of the important queries, the shortest path query over an uncertain graph has attracted much attention of researchers due to its wide applications. Although there are some e？cient solutions addressing this problem, all existing models ignore an important property existing in uncertain graphs： the correlation among the edges sharing the same vertex. In this paper, we apply Markov network to model the hidden correlation in uncertain graphs and compute the shortest path. Unfortunately, calculating the shortest path and corresponding probability over uncertain graphs modeled by Markov networks is a #P-hard problem. Thus, we propose a filtering-and-verification framework to accelerate the queries. In the filtering phase, we design a probabilistic shortest path index based on vertex cuts and blocks of a graph. We find a series of upper bounds and prune the vertices and edges whose upper bounds of the shortest path probability are lower than the threshold. By carefully picking up the blocks and vertex cuts, the index is optimized to have the maximum pruning capability, so that we can filter a large number of vertices which make no contribution to the final shortest path query results. In the verification phase, we develop an e？cient sampling algorithm to determine the final query answers. Finally, we verify the e？ciency and effectiveness of our solutions with extensive experiments.