基于VB.NET实现任意两点问最短路径算法

实际生活中的许多问题都可归结为图论中的求最短路径问题,Dijkstra算法是求最短路径算法中最有效的算法之一.在VB.NET编程环境下,实现了Dijkstra算法,根据指定的起始点和终点,得到了两点之间的最短路径长度和经过的节点.     

基于VB.NET实现任意两点间最短路径算法

实际生活中的许多问题都可归结为图论中的求最短路径问题,Dijkstra算法是求最短路径算法中最有效的算法之一。在VB.NET编程环境下,实现了Dijkstra算法,根据指定的起始点和终点,得到了两点之间的最短路径长度和经过的节点。     

改进的局部线性嵌入算法及其应用

局部线性嵌入算法（LLE）中常用欧氏距离来度量样本间相似度,而对于具有低维流形结构的高维数据,欧氏距离不能衡量流形上两点间相对位置关系。提出基于Geodesic Rank-order距离的局部线性嵌入算法（简称GRDLLE）。应用最短路径算法（Dijkstra算法）找到最短路径长度来近似计算任意两个样本间的测地线距离,计算Rank-order距离用于LLE算法的相似性度量。将GRDLLE算法、其他改进LLE的流形学习算法及2DPCA算法在ORL与Yale数据集上进行对比实验,对数据用GRDLLE算法进行降维后人脸识别率有所提高,结果表明GRDLLE算法具有很好的降维效果。     

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。     

多维代价图模型上最优路径查询问题的研究

近年来,图数据模型被广泛地用于刻画现实世界中各种各样的实体间的复杂关系.最短路径查询是图研究领域中一类非常重要的查询并有着广泛的应用.然而,目前大多数关于最短路径的查询都是定义在单代价(权重)图模型下的.现实世界中,基于单一代价所选择的最短路径并不明智,比如路程最短的路径需要花费极高的费用.该文中,作者介绍了多维代价图模型的概念,并给出了多维代价图模型下基于函数的最优路径的定义.现有的计算最短路径的方法都利用了最短路径的子路径最优的性质:最短路径上的任意两点间的子路径是这两点的最短路径.因此,在计算最短路径的过程中,对访问过的每个顶点,只需保留起点到该点的最短路径即可.不幸的是,多维代价图模型下,当评分函数是非线性的时候,子路径最优的性质并不成立.因此,目前的方法均不能应用于多维代价图模型下基于函数的最优路径查询问题.该文给出了一个best-first search分支界限法并给出3种优化策略.进一步,给出了一个顶点过滤算法,该算法能从图中过滤掉大部分不属于最优路径的顶点.最后,用真实数据集上的实验验证了算法的有效性.     

Dijkstra算法在城市道路网络中的应用

本文介绍了一个利用自然语言处理技术进行城市交通查询的系统.在研究城市道路网络特征基础上,建立城市道路网络模型及其数据库,应用Dijkstra算法对城市道进行最短路径查询,该算法是从起点和终点分别用二叉树按起点到终点和终点到起点的方向进行搜索,并得到良好的查询结果.     

切换到高一层路网最近四个点的最短路算法

针对基于大规模图的最短路问题求解速度慢的问题,提出了一个基于路网等级的求最短路的快速近似算法。该算法首先求出高一层路网到起点的4个最近点和到终点的4个最近点及最短路径,由高一层路网形成的子图T再加上这8个最短路径形成图T',在T'上求起点到终点的最短路。这种设计使得该算法适合在超大规模图上求解,理论上也证明了精度可控,同时预处理数据也是可行的,从而使两点间最短路的求解速度大大提高。在纽约公路网上的测试结果说明了该算法的有效性和合理性。     

多仓储机器人协同路径规划与作业避碰

针对多仓储移动机器人协同作业问题,提出了一种基于全局规划和局部调整的路径规划方法,以获得较短、无碰、避障的可行路径.在路径规划时根据当前节点到终点的距离和局部路径与起点至终点的欧氏路径的夹角设计新启发式函数,驱使机器人沿最短路行进;根据可选节点的数量提出避障规则,提高避障能力;依据路径长度对信息素进行比较更新,以精炼搜索空间、提高收敛性能,对蚁群算法加以改进寻找各自最优路径.在作业避碰时设计避碰规则有效解决仓储机器人间作业碰撞,找到最优或近优路径组合.实验结果表明了本方法的可行性、有效性.     

一种基于顺序多维定标的无锚点定位算法的研究

针对经典多维定标无锚点定位(MDS(C))算法在节点定位精度方面的不足,提出了一种基于顺序多维定标的无锚点定位(MDS(O))算法。该算法假定节点对之间的最短路径距离和欧氏距离存在单调性关系,避免了MDS(C)中节点对之间的最短路径距离和欧氏距离线性关系难以确定的缺陷。理论分析和仿真结果表明:MDS(O)能够提高平均定位精度1.04%～38.2%,有效地实现了节点定位。     

移动机器人最优路径规划方法

针对移动机器人路径规划效率低的问题,提出了一种基于改进的最短路径快速算法的移动机器人最优路径规划方法。该方法在障碍Voronoi图基础上根据规则将起始点与终点加入该图以得到无碰撞路径图,然后采用改进的最短路径快速算法搜索从起始点到终点的最优无碰撞路径。仿真结果表明,采用该改进算法后,移动机器人能够沿着最优无碰撞路径前进,快速达到终点。     

参考节点嵌入最短距离估算在图聚类中的应用

为解决社会关系网络图中节点没有坐标值、不能采用传统的欧几里得距离和曼哈坦距离进行聚类的问题,提出采用最短路径算法,来衡量点与点之间的相异度.针对最短路径算法具有时间复杂度大的缺点,引入基于参考节点嵌入的最短距离估算思想来估算两点之间的近似距离.在此基础上,针对DBLP数据集构成的社会关系网络图进行聚类,使用基于划分的k-medoids算法,分别采用以上两种距离算法,比较其优劣.实验证明改进后的算法和最短路径算法中的Dijkstra 算法相比,距离误差率小,时间复杂度大大降低,在提高效率的同时,取得了同样好的聚类效果.     

The optimal sequenced route query

Real-world road-planning applications often result in the formulation of new variations of the nearest neighbor (NN) problem requiring new solutions. In this paper, we study an unexplored form of NN queries named optimal sequenced route (OSR) query in both vector and metric spaces. OSR strives to find a route of minimum length starting from a given source location and passing through a number of typed locations in a particular order imposed on the types of the locations. We first transform the OSR problem into a shortest path problem on a large planar graph. We show that a classic shortest path algorithm such as Dijkstra’s is impractical for most real-world scenarios. Therefore, we propose LORD, a light threshold-based iterative algorithm, which utilizes various thresholds to prune the locations that cannot belong to the optimal route. Then we propose R-LORD, an extension of LORD which uses R-tree to examine the threshold values more efficiently. Finally, for applications that cannot tolerate the Euclidean distance as estimation and require exact distance measures in metric spaces (e.g., road networks) we propose PNE that progressively issues NN queries on different point types to construct the optimal route for the OSR query. Our extensive experiments on both real-world and synthetic datasets verify that our algorithms significantly outperform a disk-based variation of the Dijkstra approach in terms of processing time (up to two orders of magnitude) and required workspace (up to 90% reduction on average).     

图聚类的算法及其在社会关系网络中的应用

研究图聚类的算法问题。在基于划分的图聚类中,重点比较点与点之间距离的计算方法及其对聚类结果的影响。由于社会关系网络图中点没有坐标值,所以不能使用欧几里得距离和曼哈坦距离。使用k-medoids聚类算法时,分别采用最短距离和随机漫步距离算法,将DBLP数据集构成的社会关系网络图分类成各个子图,通过实验数据验证两种算法的优劣。实验证明最短距离算法获得聚类效果更为理想,达到了较好的分类效果。     

A multi-resolution surface distance model for <Emphasis Type="Italic">k</Emphasis>-NN query processing

A spatial k-NN query returns k nearest points in a point dataset to a given query point. To measure the distance between two points, most of the literature focuses on the Euclidean distance or the network distance. For many applications, such as wildlife movement, it is necessary to consider the surface distance, which is computed from the shortest path along a terrain surface. In this paper, we investigate the problem of efficient surface k-NN (sk-NN) query processing. This is an important yet highly challenging problem because the underlying environment data can be very large and the computational cost of finding the shortest path on a surface can be very high. To minimize the amount of surface data to be used and the cost of surface distance computation, a multi-resolution surface distance model is proposed in this paper to take advantage of monotonic distance changes when the distances are computed at different resolution levels. Based on this innovative model, sk-NN queries can be processed efficiently by accessing and processing surface data at a just-enough resolution level within a just-enough search region. Our extensive performance evaluations using real world datasets confirm the efficiency of our proposed model.     

无回路网络中最短路问题的高效算法

无回路网络是一类重要的网络,给出在无回路网络中求解最短路树形图和任意顶点对间最短路的高效算法。该算法将顶点进行重新编号,结合广度优先探索法,从源顶点出发依次搜索每个顶点的所有出弧,并在弧的头部进行权值变换操作,可以得到最短路树形图和任意顶点对间最短路,算法复杂度分别为O(m)和O(m(n-m1/2))。该算法思想简便、复杂度低、易于操作。 关键词：     

Parallel Mesh Algorithms for Grid Graph Shortest Paths with Application to Separation of Touching Chromosomes

The grid graph shortest path problem has many applications. In this paper, we present practical mesh algorithms using a local cost-reducing operation for various forms of the grid graph shortest path problem. The algorithms are very simple and can easily mark the vertices on shortest paths between any two vertices. The time complexity of the algorithm is proportional to the maximum length of the shortest paths with a very small multiplicative constant. Also in this paper, we discuss the application of the parallel algorithms in automatic chromosome analysis to intelligently split touching chromosomes. We identify local features useful for finding a potential path to separate touching chromosomes. We then define a distance measure based on the local features and find the best splitting path to cut touching chromosomes. The splitting algorithm only uses local information and is highly parallel.     

不可达顶点剪枝算法及其在最短路径中的应用

[k]步可达性查询用于回答图[G]中从顶点[u]到达顶点[v]最多[k]步是否存在路径,但其多用于无权图的可达性研究。针对加权图,在图中构建了最早到达、逆向最早到达和最晚到达等三个索引,并应用这三个索引实现对不可达顶点的快速剪枝,从而有效地缩减了加权图的规模。运用该方法建立索引并剪枝顶点的时间复杂度与空间复杂度分别为[O(n+e)]和[O(n)],这里[n]和[e]分别为图中顶点的数目和边的数目。该方法可以与Dijkstra算法、Floyd算法和A*算法等多种传统算法相结合,并应用于最短路径求解,从而提高传统算法计算性能。最后以物流配送网络为例进行了实验验证,实验结果表明提出的方法可以正确并高效地对不必要计算的顶点进行剪枝,从而加快了最短路径求解速度,验证了提出方法的有效性。     

The exact distance to destination in undirected world

Shortest distance queries are essential not only in graph analysis and graph mining tasks but also in database applications, when a large graph needs to be dealt with. Such shortest distance queries are frequently issued by end-users or requested as a subroutine in real applications. For intensive queries on large graphs, it is impractical to compute shortest distances on-line from scratch, and impractical to materialize all-pairs shortest distances. In the literature, 2-hop distance labeling is proposed to index the all-pairs shortest distances. It assigns distance labels to vertices in a large graph in a pre-computing step off-line and then answers shortest distance queries on-line by making use of such distance labels, which avoids exhaustively traversing the large graph when answering queries. However, the existing algorithms to generate 2-hop distance labels are not scalable to large graphs. Finding an optimal 2-hop distance labeling is NP-hard, and heuristic algorithms may generate large size distance labels while still needing to pre-compute all-pairs shortest paths. In this paper, we propose a multi-hop distance labeling approach, which generates a subset of the 2-hop distance labels as index off-line. We can compute the multi-hop distance labels efficiently by avoiding pre-computing all-pairs shortest paths. In addition, our multi-hop distance labeling is small in size to be stored. To answer a shortest distance query between two vertices, we first generate the query-specific small set of 2-hop distance labels for the two vertices based on our multi-hop distance labels stored and compute the shortest distance between the two vertices based on the 2-hop distance labels generated on-line. We conducted extensive performance studies on large real graphs and confirmed the efficiency of our multi-hop distance labeling scheme.     

Estimating graph distance and centrality on shared nothing architectures

We present a parallel toolkit for pairwise distance computation in massive networks. Computing the exact shortest paths between a large number of vertices is a costly operation, and serial algorithms are not practical for billion‐scale graphs. We first describe an efficient parallel method to solve the single source shortest path problem on commodity hardware with no shared memory. Using it as a building block, we introduce a new parallel algorithm to estimate the shortest paths between arbitrary pairs of vertices. Our method exploits data locality, produces highly accurate results, and allows batch computation of shortest paths with 7% average error in graphs that contain billions of edges. The proposed algorithm is up to two orders of magnitude faster than previously suggested algorithms and does not require large amounts of memory or expensive high‐end servers. We further leverage this method to estimate the closeness and betweenness centrality metrics, which involve systems challenges dealing with indexing, joining, and comparing large datasets efficiently. In one experiment, we mined a real‐world Web graph with 700 million nodes and 12 billion edges to identify the most central vertices and calculated more than 63 billion shortest paths in 6 h on a 20‐node commodity cluster. Copyright © 2014 John Wiley & Sons, Ltd.     

大图上跳数受限的可达查询算法研究与优化

判断有向图上两个顶点之间是否存在一条路径是一个经典问题,而对于一些路由规划和图分析等实际应用,要求查找是否存在跳数受限的可达路径,这是一个变种的图可达查询问题.对于大图上跳数受限的查询算法,不仅仅要对大图查询的时间效率和空间效率进行权衡,而且还要利用跳数受限的特性进行优化.普通的可达查询算法存在小度数顶点索引项占用空间过多的问题,造成空间浪费严重.为此我们提出了一种面向跳数受限的2-hop部分索引方法,采用改进的索引方法并结合局部搜索,实现跳数受限的有效可达性查询.实验结果表明,在Orkut社交网络数据集上与已有算法相比,该算法索引空间节省了32％,同时查询时间略微增加,使得我们算法可以计算更大规模图的跳数受限可达问题.