低冗余计算的可达性查询保持图压缩策略

针对可达性查询保持图压缩（QPGC）算法存在冗余计算的问题,提出了一种高性能压缩策略。在求解顶点的祖先后代集阶段,针对普通图数据,提出一种基于拓扑排序的求解算法TSB,首先将图数据顶点拓扑排序,然后沿拓扑序列顺序（逆序）求解顶点的祖先（后代）集,避免了求解顺序不明确导致的冗余计算;针对最长路径较短的图数据,提出一种基于图聚合运算的求解算法AGGB,可在确定次数的聚合运算内完成顶点的祖先和后代集的求解。在求解可达性等价类阶段,提出一种分段统计剪枝算法PSP,先对祖先后代集分段统计,再比较统计值以实现粗匹配,剪除了部分不必要的精细匹配。实验结果表明,与QPGC算法相比：在祖先后代集求解阶段,TSB和AGGB在不同数据集上的性能平均提升94.22%和90.00%;在求解可达性等价类阶段,PSP算法在大部分数据集上性能提升超过70%;随着数据集的增大,TSB和AGGB配合PSP算法,性能提升了近28倍。理论分析和模拟实验表明,该策略与QPGC算法相比冗余计算更少、压缩速度更快。     

一种基于图归约的XPath高性能流数据查询方法

作为网络数据交换和数据共享的标准,XML数据越来越多地用于表示应用系统的流数据。然而,受制于流数据处理有限空间开销等特征,如何高效地实现这种查询成为值得探讨的问题。与传统的基于自动机或层次栈方法不同,文中提出了一种基于图归约的XML查询自动机(GRAT),采用一种图结构来表示针对不同XML流元素的子查询任务之间的关系,通过图的归约变化来实现XPath查询。实验结果表明,基于GRAT的查询算法能够高效地完成复杂的XML查询,流数据处理的吞吐量达到了较高水平。     

Using graph parsing for automatic graph drawing

This paper presents a procedure for automatically drawing directed graphs. Our system, Clan-based Graph Drawing Tool (CG), uses a unique clan-based graph decomposition to determine intrinsic substructures (clans) in the graph and to produce a parse tree. The tree is given attributes that specify the node layout. CG then uses tree properties with the addition of “routing nodes” to route the edges. The objective of the system is to provide, automatically, an aesthetically pleasing visual layout for arbitrary directed graphs. The prototype has shown the strengths of this approach. The innovative strategy of clan-based graph decomposition is the first digraph drawing technique to analyze locality in the graph in two dimensions. The typical approach to drawing digraphs uses a single dimension, level, to arrange the nodes     

Cluster query: a new query pattern on temporal knowledge graph

A temporal knowledge graph (TKG) is theoretically a temporal graph. Recently, systems have been developed to support snapshot queries over temporal graphs. However, snapshot queries can only give separate answers. To retrieve forward-backward correlation facts from temporal knowledge graph, cluster query is proposed in this paper. To deal with the query, the logical view and physical model are presented. Subsequently, five corresponding basic query patters of unit matching are studied, and then the complete matchings are also addressed. To improve the query performance, index-based methods and pruning strategies are adopted. Experiments are conducted to evaluate cluster queries on three real datasets. The experimental results show the effectiveness and efficiency of cluster queries on temporal knowledge graphs.

     

Searching Steiner trees for web graph query

The enormous growth in information technology has revolutionized the way people can access information sources. Web search engines have played an important role to support what the user wants precisely and efficiently from the vast web database. Different from conventional search engine approaches, searching the structure of the web, where the answer comprises more than a single page connected by hyperlinks, needs to be meritoriously developed. We propose Linear Programming models in order to generate the optimal structured web objects searching for relevant web graphs. In the model, the web objects with node and edge weights that represent the ranking measures for Webpages and hyperlinks are devised to rank the relevance in terms of keyword vectors. We also developed a tree-filtering algorithm and top-k Steiner tree algorithm that is used to provide the search recommendations in practical applications. With real web databases, the experimental study shows that the LP approach outperforms the conventional search engines with respect to execution time and quality of results.     

A simple graph theoretic characterization of reachability for positive linear systems

In this paper we consider discrete-time linear positive systems, that is systems defined by a pair (A,B) of non-negative matrices. We study the reachability of such systems which in this case amounts to the freedom of steering the state in the positive orthant by using non-negative control sequences. This problem was solved recently [Canonical forms for positive discrete-time linear control systems, Linear Algebra Appl., 310 (2000) 49]. However we derive here necessary and sufficient conditions for reachability in a simpler and more compact form. These conditions are expressed in terms of particular paths in the graph which is naturally associated with the system.     

Extensions to query languages for graph traversal problems

Extensions to database query languages for retrievals that involve inferencing on the nodes and edges of a graph are surveyed. Common types of inferencing are to find paths between two nodes, compute a value for a path such as a distance or an elapsed time, and to choose among alternative paths. The survey is based on the data model (relational or functional), method of extension (iteration, recursion, or special operators), interface style (string or tabular), and restrictions (data- and problem-oriented). The Quel, objected-oriented functional data, G-Whin, and Alpha languages are examined in detail with different values for these properties. The characteristics of other languages are summarized in several tables. The results of the survey indicate the diversity of language extensions and the need to provide data-model and query-language features to address such problems     

A graph theoretical approach to determine a join reducer sequencein distributed query processing

Semijoin has traditionally been relied upon to reduce the cost of data transmission for distributed query processing. However, judiciously applying join operations as reducers can lead to further reduction in the amount of data transmission required. In view of this fact, we explore the approach of using join operations as reducers in distributed query processing. We first show that the problem of determining a sequence of join operations for a query can be transformed to that of finding a specific type of set of cuts to the corresponding query graph, where a cut to a graph is a partition of nodes in that graph. Then, in light of this concept, we prove that the problem of determining the optimal sequence of join operations for a given query graph is of exponential complexity, thus justifying the necessity of applying heuristic approaches to solve this problem. By mapping the problem of determining a sequence of join reducers into the one of finding a set of cuts, we develop (for tree and general query graphs, respectively) efficient heuristic algorithms to determine a join reducer sequence for distributed query processing. The algorithms developed are based on the concept of divide and conquer and are of polynomial time complexity. Simulation is performed to evaluate these algorithms     

Robot reachability problem: A nonlinear optimization approach

The reachability of a robot manipulator to a target is defined as its ability to move its joints and links in free space in order for its hand to reach the given target. This paper presents a way of testing the reachability of a robot to given target. The target could be a three dimensional object represented by a cuboid, a line or merely a point.The reachability test problem is transformed into a nonlinear optimization problem, which is solved by using the Tunneling Algorithm [1–3].The paradigm of the Tunneling Algorithm is described in detail. Several examples of testing the reachability of two robots to given targets are presented and the results are compared with that of the existing RGRG algorithm [5]. The results of comparisons show that the Tunneling Algorithm is better than the RGRG algorithm. It can always obtain the correct answers of testing, and it is effective and suitable to solve the reachability test problem.This project is partially supported by a grant from Martin Marietta (ORNL) 19x-55902V. Also this project is partially funded by ONR grant N00014-94-1-0343.     

Index design and query processing for graph conductance search

Graph conductance queries, also known as personalized PageRank and related to random walks with restarts, were originally proposed to assign a hyperlink-based prestige score to Web pages. More general forms of such queries are also very useful for ranking in entity-relation (ER) graphs used to represent relational, XML and hypertext data. Evaluation of PageRank usually involves a global eigen computation. If the graph is even moderately large, interactive response times may not be possible. Recently, the need for interactive PageRank evaluation has increased. The graph may be fully known only when the query is submitted. Browsing actions of the user may change some inputs to the PageRank computation dynamically. In this paper, we describe a system that analyzes query workloads and the ER graph, invests in limited offline indexing, and exploits those indices to achieve essentially constant-time query processing, even as the graph size scales. Our techniques—data and query statistics collection, index selection and materialization, and query-time index exploitation—have parallels in the extensive relational query optimization literature, but is applied to supporting novel graph data repositories. We report on experiments with five temporal snapshots of the CiteSeer ER graph having 74–702 thousand entity nodes, 0.17–1.16 million word nodes, 0.29–3.26 million edges between entities, and 3.29–32.8 million edges between words and entities. We also used two million actual queries from CiteSeer’s logs. Queries run 3–4 orders of magnitude faster than whole-graph PageRank, the gap growing with graph size. Index size is smaller than a text index. Ranking accuracy is 94–98% with reference to whole-graph PageRank.     

GraphSET,a tool for simultaneous graph drawing

Problems in simultaneous graph drawing involve the layout of several graphs on a shared vertex set. This paper describes a Graph Simultaneous Embedding Tool, GraphSET, designed to allow the investigation of a wide range of graph embedding problems. GraphSET can be used in the study of several variants of simultaneous embedding including simultaneous geometric embedding, simultaneous embedding with fixed edges, and colored simultaneous embedding with the vertex set partitioned into color classes. The tool has three primary uses: (i) studying theoretical problems in simultaneous graph drawing through the production of examples and counterexamples, (ii) producing layouts of given classes of graphs using built‐in implementations of known algorithms, and (iii) providing a platform for development and implementation of new algorithms and data structures for all variants of simultaneous graph embedding. We also describe the design decisions involved in the construction of GraphSET in terms of the requirements dictated by its applications. GraphSET along with movies illustrating its utility are available at http://graphset.cs.arizona.edu . Copyright © 2010 John Wiley & Sons, Ltd.     

Clustering high dimensional data: A graph-based relaxed optimization approach

There is no doubt that clustering is one of the most studied data mining tasks. Nevertheless, it remains a challenging problem to solve despite the many proposed clustering approaches. Graph-based approaches solve the clustering task as a global optimization problem, while many other works are based on local methods. In this paper, we propose a novel graph-based algorithm “GBR” that relaxes some well-defined method even as improving the accuracy whilst keeping it simple. The primary motivation of our relaxation of the objective is to allow the reformulated objective to find well distributed cluster indicators for complicated data instances. This relaxation results in an analytical solution that avoids the approximated iterative methods that have been adopted in many other graph-based approaches. The experiments on synthetic and real data sets show that our relaxation accomplishes excellent clustering results. Our key contributions are: (1) we provide an analytical solution to solve the global clustering task as opposed to approximated iterative approaches; (2) a very simple implementation using existing optimization packages; (3) an algorithm with relatively less computation time over the number of data instances to cluster than other well defined methods in the literature.     

An approximate algorithm for top-k closest pairs join query in large high dimensional data

In this paper we present a novel approximate algorithm to calculate the top-k closest pairs join query of two large and high dimensional data sets. The algorithm has worst case time complexity and space complexity and guarantees a solution within a factor of the exact one, where t  {1, 2, … , ∞} denotes the Minkowski metrics L_t of interest and d the dimensionality. It makes use of the concept of space filling curve to establish an order between the points of the space and performs at most d + 1 sorts and scans of the two data sets. During a scan, each point from one data set is compared with its closest points, according to the space filling curve order, in the other data set and points whose contribution to the solution has already been analyzed are detected and eliminated. Experimental results on real and synthetic data sets show that our algorithm behaves as an exact algorithm in low dimensional spaces; it is able to prune the entire (or a considerable fraction of the) data set even for high dimensions if certain separation conditions are satisfied; in any case it returns a solution within a small error to the exact one.     

面向图数据的结构化正则路径查询方法

正则路径查询是一种应用正则表达式在图数据上进行查询的技术,通常利用有限状态自动机实现查询匹配。现有正则路径查询方法的匹配结果为顶点对的序列,未能充分保留图的结构,为了解决这一问题,提出了一种面向图数据的结构化正则路径查询方法,通过在不同的序列间加以结构化约束,使得查询结果由路径转变为子图。为了实现这一目的,首先定义了一种结构化的正则路径查询语言,并设计了结构化的查询解析以及基于此结构的匹配算法。实验在模拟数据集和真实数据集上进行了测试与分析,验证了网络规模对查询速度的影响,并设置了对照实验。实验结果表明,提出方法能够在保证满足正则表达式约束的前提下实现结构化查询。     

PathQuery Pregel: high-performance graph query with bulk synchronous processing

Pattern Analysis and Applications - High-performance graph query systems are a scalable way to mine information in Knowledge Graphs, especially when the queries benefit from a high-level expressive...     

The topological drawing of a graph: Construction methods

This paper considers construction algorithms for the topological 2-D drawing of a graph. These algorithms allow to store, describe and modify the existing information on the drawing of a graph. Finally, we introduce necessary notions and structures to solve the problem of the topological 2-D drawing of a graph.     

A fuzzy genetic algorithm for automatic orthogonal graph drawing

This paper reflects results of research related to developing a new methodology for automatic graph drawing based on applying genetic algorithms. The methodology has permitted the elaboration of a hybrid technique that combines the most popular, classical, topology-shape-metric approach to orthogonal drawings on the grid and a genetic algorithm that is directed, in its evolutionary process, at multicriteria decision making in a fuzzy environment. In the traditional use of the topology-shape-metric approach, a single fixed planar embedding is obtained in the planarization step. Thereafter this embedding is subjected to the orthogonalization and compaction steps. However, this sequence does not guarantee that the fixed planar embedding will generate a final drawing of a good quality. Moreover, every topology-shape-metric step is classified as a NP-hard problem, and choices as well as heuristics used in previous stages have a direct impact on subsequent ones. Taking this into account, the developed hybrid technique generates a greater number of planar embeddings by varying the order of edges’ insertion when forming the planar embeddings in planarization step. Thus, the problem is formulated as a permutation-based combinatorial optimization problem. The genetic algorithm is applied at the planarization step of the topology-shape-metric. This allows one to generate the population with the corresponding number of planar embeddings. Each planar embedding obtained in the planarization step is submitted to the orthogonalization and compaction. Their results serve for applying the procedures of multicriteria decision making in a fuzzy environment. Thus, in the evolutionary process, the genetic algorithm is able to select individuals, which provide more harmonious solutions (relatively of the solutions obtained with traditional applying the topology-shape-metric approach) from the point of view of the aesthetic criteria that are usually utilized at the three steps of automatic graph drawing. This is convincingly demonstrated by experimental results given in the paper.