Efficient processing of shortest path queries in evolving graph sequences

In many applications, information is best represented as graphs. In a dynamic world, information changes and so the graphs representing the information evolve with time. We propose that historical graph-structured data be maintained for analytical processing. We call a historical evolving graph sequence an EGS. We observe that in many applications, graphs of an EGS are large and numerous, and they often exhibit much redundancy among them. We study the problem of efficient shortest path query processing on an EGS and put forward a solution framework called FVF. Two algorithms, namely, FVF-F and FVF-H, are proposed. While the FVF-F algorithm works on a sequence of flat graph clusters, the FVF-H algorithm works on a hierarchy of such clusters. Through extensive experiments on both real and synthetic datasets, we show that our FVF framework is highly efficient in shortest query processing on EGSs. Comparing FVF-F and FVF-H, the latter gives a larger speedup, is more flexible in terms of memory requirements, and is far less sensitive to parameter values.     

Optimization and evaluation of shortest path queries

We investigate the problem of how to evaluate efficiently a collection of shortest path queries on massive graphs that are too big to fit in the main memory. To evaluate a shortest path query efficiently, we introduce two pruning algorithms. These algorithms differ on the extent of materialization of shortest path cost and on how the search space is pruned. By grouping shortest path queries properly, batch processing improves the performance of shortest path query evaluation. Extensive study is also done on fragment sizes, cache sizes and query types that we show that affect the performance of a disk-based shortest path algorithm. The performance and scalability of proposed techniques are evaluated with large road systems in the Eastern United States. To demonstrate that the proposed disk-based algorithms are viable, we show that their search times are significant better than that of main-memory Dijkstra's algorithm.     

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).     

基于MapX的电子地图路径规划软件设计

文章设计了基于MapX的可视化电子地图路径规划软件,实现了地图操作中的放大、缩小、漫游、测距、图层控制等功能。该软件可作为交通道路电子导航使用,根据Dijkstra算法完成任意起始点和目的地之间的最短路径计算,提供求懈最短路径功能,根据蚁群算法求解真实路网的路径规划问题,可以在指定的节点范围内寻找一条最优路径,实现路径规划功能。该软件操作简单方便,用户很容易就可以掌握该软件的使用,实现旅游信息的快速查询,给用户带来了方便快捷的信息服务。     

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.     

k-Multi-preference query over road networks

Nowadays, the road network has gained more and more attention in the research area of databases. Existing works mainly focus on standalone queries, such as k-nearest neighbor queries over a single type of objects (e.g., facility like restaurant or hotel). In this paper, we propose a k-multi-preference (kMP) query over road networks, involving complex query predicates and multiple facilities. In particular, given a query graph, a kMP query retrieves of the top-k groups of vertices (of k facility types) satisfying the label constraints and their aggregate distances are the smallest. A naïve solution to this problem is to enumerate all combinations of vertices with k possible facility types and then select the one with the minimum sum distance. This method, however, incurs rather high computation cost due to exponential possible combinations. In addition, the existing solutions to other standalone queries are for a single type of facilities and cannot be directly used to answer kMP queries. Therefore, in this paper, we propose an efficient approach to process a kMP query, which utilizes an index with bounded space and reduces the computation cost of the shortest path queries. We also design effective pruning techniques to filter out false alarms. Through our extensive experiments, we demonstrate the efficiency and effectiveness of our proposed solutions.     

Shrink: Distance preserving graph compression

The ever increasing size of graphs makes them difficult to query and store. In this paper, we present Shrink, a compression method that reduces the size of the graph while preserving the distances between the nodes. The compression is based on the iterative merging of the nodes. During each merging, a system of linear equations is solved to define new edge weights in a way that the new weights have the least effect on the distances. Merging nodes continues until the desired size for the compressed graph is reached. The compressed graph, also known as the coarse graph, can be queried without decompression. As the complexity of distance-based queries such as shortest path queries is highly dependent on the size of the graph, Shrink improves the performance in terms of time and storage. Shrink not only provides the length of the shortest path but also identifies the nodes on the path. The approach has been applied to both weighted and unweighted graphs including road network, friendship network, collaboration network, web graph and social network. In the experiment, a road network with more than 2.5 million nodes is reduced to fifth while the average relative error is less than 1%.     

Cellular matrix model for parallel combinatorial optimization algorithms in Euclidean plane

We propose a parallel computation model, called cellular matrix model (CMM), to address large-size Euclidean graph matching problems in the plane. The parallel computation takes place by partitioning the plane into a regular grid of cells, each cell being affected to a single processor. Each processor operates on local data, starting from its cell location and extending its search to the neighborhood cells in a spiral search way. In order to deal with large-size problems, memory size and processor number are fixed as O(N), where N is the problem size. Then one key point is that closest point searching in the plane is performed in O(1) expected time for uniform or bounded distribution, for each processor independently. We define a generic loop that models the parallel projection between graphs and their matching, as executed by the many cells at a given level of computation granularity. To illustrate its efficacy and versatility, we apply the CMM, on GPU platforms, to two problems in image processing: superpixel segmentation and stereo matching energy minimization. Firstly, we propose an extended version of the well-known SLIC superpixel segmentation algorithm, which we call SPASM algorithm, by using a parallel 2D self-organizing map instead of k-means algorithm. Secondly, we investigate the idea of distributed variable neighborhood search, and propose a parallel search heuristic, called distributed local search (DLS), for global energy minimization of stereo matching problem. We evaluate the approach with regards to the state-of-the-art graph cut and belief propagation algorithms. For each problem, we argue that the parallel GPU implementation provides new competitive quality/time trade-offs, with substantial acceleration factors as the problem size increases.     

Fast graph similarity search via hashing and its application on image retrieval

Similarity search in graph databases has been widely investigated. It is worthwhile to develop a fast algorithm to support similarity search in large-scale graph databases. In this paper, we investigate a k-NN (k-Nearest Neighbor) similarity search problem by locality sensitive hashing (LSH). We propose an innovative fast graph search algorithm named LSH-GSS, which first transforms complex graphs into vectorial representations based on prototypes in the database and later accelerates a query in Euclidean space by employing LSH. Because images can be represented as attributed graphs, we propose an approach to transform attributed graphs into n-dimensional vectors and apply LSH-GSS to execute further image retrieval. Experiments on three real graph datasets and two image datasets show that our methods are highly accurate and efficient.     

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.     

Querying multimedia presentations based on content

Considers the problem of querying multimedia presentations based on content information. Multimedia presentations are modeled as presentation graphs, which are directed acyclic graphs that visually specify the presentations. We present a graph data model for the specification of multimedia presentations and discuss query languages as effective tools to query and manipulate multimedia presentation graphs with respect to content information. To query the information flow throughout a multimedia presentation, as well as in each individual multimedia stream, we use revised versions of temporal operators Next, Connected and Until, together with path formulas. These constructs allow us to specify and query paths along a presentation graph. We present an icon-based graphical query language, GVISUAL, that provides iconic representations for these constructs and a user-friendly graphical interface for query specification. We also present an OQL-like language, GOQL (Graph OQL), with similar constructs, that allows textual and more traditional specifications of graph queries. Finally, we introduce GCalculus (Graph Calculus), a calculus-based language that establishes the formal grounds for the use of temporal operators in path formulas and for querying presentation graphs with respect to content information. We also discuss GCalculus/S (GCalculus with Sets) which avoids highly complex query expressions by eliminating the universal path quantifier, the negation operator and the universal quantifier. GCalculus/S represents the formal basis for GVISUAL, i.e. GVISUAL uses the constructs of GCalculus/S directly     

Location‐dependent generalization of road networks based on equivalent destinations

Suppose a user located at a certain vertex in a road network wants to plan a route using a wayfinding map. The user's exact destination may be irrelevant for planning most of the route, because many destinations will be equivalent in the sense that they allow the user to choose almost the same paths. We propose a method to find such groups of destinations automatically and to contract the resulting clusters in a detailed map to achieve a simplified visualization. We model the problem as a clustering problem in rooted, edge‐weighted trees. Two vertices are allowed to be in the same cluster if and only if they share at least a given fraction of their path to the root. We analyze some properties of these clusterings and give a linear‐time algorithm to compute the minimum‐cardinality clustering. This algorithm may have various other applications in network visualization and graph drawing, but in this paper we apply it specifically to focus‐and‐context map generalization. When contracting shortest‐path trees in a geographic network, the computed clustering additionally provides a constant‐factor bound on the detour that results from routing using the generalized network instead of the full network. This is a desirable property for wayfinding maps.     

道路网络中k路径最近邻居针对两种目标点的应用

提出一种道路网络中针对两种不同类型目标点的k组路径最近邻居查询,这是一种新的查询:给出用户希望到达的终点位置以及两组目标点集合,这种查询返回连接用户当前位置和终点位置的最短路径,以及相对于这条最短路径的k组路径最近邻居,每组包含两个不同类型的目标点,将这种查询命名为k-PNNT.提出了一种典型的过滤-精炼算法得到k-PNNT及对应的最短路径,并且在实际道路网络中进行了实验.实验证明,算法可行,有效.     

Applying the shortest-path-counting problem to evaluate the importance of city road segments and the connectedness of the network-structured system

We consider the shortest‐path‐counting problem (SPCP), which asks how many shortest paths is each edge of a network contained in? There are n(n?1) shortest paths in a network with n nodes, so among all these shortest paths the SPCP requires us to count the number of shortest paths passing through each edge. We obtain theoretical results in the form of explicit expressions for special types of networks such as trees, grid type, circular type, etc. We apply the SPCP to measure the importance of city road segments, which will certainly contribute to estimate the traffic congestion of the city road segments. Then we propose a quantitative method for evaluating the stable connectedness of the network‐structured system using shortest‐path‐counting methods. We define the stable‐connection function and the expected stable‐connection function for the network‐structured system. Then we derive some theoretical results for some special types of network such as single path, cycle graph, and complete graph. Several properties and characteristics of the stable‐connection function are also shown with some theoretical results. We show the application of the Monte Carlo method to estimate the expected stable‐connection function. This method can be applied to measure the strength of connectedness of the Japanese road network system.     

Extending SPARQL with regular expression patterns (for querying RDF)

RDF is a knowledge representation language dedicated to the annotation of resources within the framework of the semantic web. Among the query languages for RDF, SPARQL allows querying RDF through graph patterns, i.e., RDF graphs involving variables. Other languages, inspired by the work in databases, use regular expressions for searching paths in RDF graphs. Each approach can express queries that are out of reach of the other one. Hence, we aim at combining these two approaches. For that purpose, we define a language, called PRDF (for “Path RDF”) which extends RDF such that the arcs of a graph can be labeled by regular expression patterns. We provide PRDF with a semantics extending that of RDF, and propose a correct and complete algorithm which, by computing a particular graph homomorphism, decides the consequence between an RDF graph and a PRDF graph. We then define the PSPARQL query language, extending SPARQL with PRDF graph patterns and complying with RDF model theoretic semantics. PRDF thus offers both graph patterns and path expressions. We show that this extension does not increase the computational complexity of SPARQL and, based on the proposed algorithm, we have implemented a correct and complete PSPARQL query engine.     

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。     

Shortest paths on dynamic graphs

Among the variants of the well-known shortest path problem, those that refer to dynamically changing graphs are theoretically interesting, as well as computationally challenging. Application-wise, there is an industrial need for computing point-to-point shortest paths on large-scale road networks whose arcs are weighted with a travelling time that depends on traffic conditions. We survey recent techniques for dynamic graph weights as well as dynamic graph topology.     

Efficient computation of distance labeling for decremental updates in large dynamic graphs

Since today’s real-world graphs, such as social network graphs, are evolving all the time, it is of great importance to perform graph computations and analysis in these dynamic graphs. Due to the fact that many applications such as social network link analysis with the existence of inactive users need to handle failed links or nodes, decremental computation and maintenance for graphs is considered a challenging problem. Shortest path computation is one of the most fundamental operations for managing and analyzing large graphs. A number of indexing methods have been proposed to answer distance queries in static graphs. Unfortunately, there is little work on answering such queries for dynamic graphs. In this paper, we focus on the problem of computing the shortest path distance in dynamic graphs, particularly on decremental updates (i.e., edge deletions). We propose maintenance algorithms based on distance labeling, which can handle decremental updates efficiently. By exploiting properties of distance labeling in original graphs, we are able to efficiently maintain distance labeling for new graphs. We experimentally evaluate our algorithms using eleven real-world large graphs and confirm the effectiveness and efficiency of our approach. More specifically, our method can speed up index re-computation by up to an order of magnitude compared with the state-of-the-art method, Pruned Landmark Labeling (PLL).     

数据库中不等式查询语句的resilience计算

针对数据库中不等式连接查询的因果关系问题,引入并实现了resilience计算,并且为了降低其在路径类型不等式连接查询中计算的时间复杂度,提出了求解resilience的动态规划（DPResi）算法。首先,根据路径类型不等式连接查询的特点及最大流最小割原理,实现了多项式时间复杂度的Min-Cut算法;然后通过将带有不等式布尔连接查询语句的溯源表达式编辑为溯源图,进而将resilience求解问题转换为溯源图中最短距离的计算问题,并结合溯源图的包含关系与最优子结构性质,运用动态规划的思想实现了线性时间复杂度的DPResi算法。在TPC-H数据集上进行了大量实验,实验结果表明,与Min-Cut算法相比,DPResi算法极大地提高了resilience计算的效率,并具有较好的扩展性。     

An elastic partial shape matching technique

We consider the problem of partial shape matching. We propose to transform shapes into sequences and utilize an algorithm that determines a subsequence of a target sequence that best matches a query. In the proposed algorithm we map the problem of the best matching subsequence to the problem of a cheapest path in a directed acyclic graph (DAG). The approach allows us to compute the optimal scale and translation of sequence values, which is a nontrivial problem in the case of subsequence matching. Our experimental results demonstrate that the proposed algorithm outperforms the commonly used techniques in retrieval accuracy.