标签约束图上的k步可达性查询

标签约束图上的k步可达性查询问题,回答了在一个标签约束图上两点之间是否存在一条长度不大于k的路径并且这条路径上的标签都在用户给定的标签集中的问题。标签约束图上的k步可达性查询问题在现实中有着广泛的应用,然而现有算法无法直接回答这个问题。因此,首先提出LK2H算法。LK2H算法主要包括构建索引和查询两个步骤。第一步是给图上的所有顶点构建一组包含k和标签信息的2-Hop索引,第二步是基于构建好的索引进行查询。在查询时,为了尽可能地为用户返回更多的信息,LK2H算法优化了一类不可达查询的返回结果：当用户无法明确所有的标签类型,不能给出完整的标签约束,进而导致查询结果为不可达时,将完整的标签集返回给用户。其次,提出优化算法LK2H+。LK2H+算法通过构建部分顶点的2-Hop索引进一步缩减索引大小和索引的构建时间,并基于构建好的索引进行查询。查询时,需要对顶点按照是否构建了索引进行分类讨论。最后,基于15个真实数据集进行测试。实验结果表明,LK2H算法和LK2H+算法都可以高效地解决标签约束图上的k步可达性查询问题。     

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。     

传递闭包算法的探讨

传递闭包是一种重要的关系运算,它在计算机系统中有着广泛的应用。本文探讨了传递闭包的计算。分析warshall算法在有向图中的意义．并给出了一个简便的有向图传递闭包算法。     

RIAIL:大规模图上的可达性查询索引方法

图被广泛用来建模在社交网络、语义网、计算生物学和软件分析中的应用.可达性查询是图数据上的一种基础查询.当前,针对图上的可达性查询已经提出了一些索引算法,但是它们不能灵活地扩展到大的图数据.因此,提出了一种索引方法RIAIL(reachability index augmented by interval labeling).RIAIL将结点的标记信息表示成四元组.前两个元素是区间标记,编码生成树的可达性信息,后两个元素编码非树边的可达性信息.RIAIL查询时只需索引且索引创建代价小.最后,通过大量真实和人工生成数据集上的实验说明,RIAIL能够高效地处理可达性查询,并且可以简单地扩展到大的图数据.     

一类递归查询问题的快速求解算法

提出一个求解一类扩充递归Ｄａｔａｌｏｇ逻辑程序的算法,论证其正确性,并讨论了算法的复杂性。该算法结合了自底向上和自顶向下的逻辑程序求解算法的优点,但比魔集算法简单,易于实现。利用宁可以解决工程数据管理中常遇到的产品零部件装配关系的递归查询问题。     

在关系DBMS上扩充传递闭包功能的方法和实现技术

现有的关系ＤＢＭＳ一般还不支持传递闭包计算功能。为了扩充这个重要功能，作者在ＯＲＡＣＬＥＤＢＭＳ上增加了一个传递闭包处理层ＳＥＴＣＳ。ＳＥＴＣＳ提供了一个ＳＱＬ的扩充版本ＳＱＬ。ＳＱＬ比ＳＱＬ增加了传递闭包的定义和查询语句。ＳＱＬ中有关传递闭包的语句由预处理接口处理，传递闭包用半质朴算法计算。为了应用的需要，除计算传递闭包外，还提供传递闭包的深度和路径等参数。作为应用的例子，ＳＥＴＣＳ已试用于民航     

求模糊相似矩阵的传递闭包的简捷算法

模糊相似矩阵传递闭包的计算在模糊聚类及语法分析等领域应用广泛.从最大树出发论述并实现了一种求模糊相似矩阵传递闭包的简捷算法.与经典的求模糊相似矩阵传递闭包的算法—平方法比较,该算法简捷,运算量小。     

在RDBMS上扩充传递闭包功能的方法和算法

目前的ＲＤＢＭＳ一般不支持传递闭包计算功能。为扩充此功能，作者提出了在原ＲＤＢＭＳ上增加传递闭包处理层ＳＥＴＣＳ，以及扩充传递闭包定义与查询语句的ＳＱＬ＊。该方案已在ＯＲＡＣＬＥ上实现并投入应用。     

基于求传递闭包的Warshall算法的改进

围绕传递闭包分析比较了著名的Warshall算法,给出了一个三角形算法。当关系矩阵是稀疏矩阵时,该算法比Warshall快。     

关于传递闭包和函数依赖完备公理系统存在的问题研究

数据依赖在数据库设计中起着十分重要的作用，自Ｃｏｄｄ提出函数依赖，Ｆａｇｉｎ引入多值依赖后，近几年来人们又根据设计中的需要引入多种新的依赖，如在工程数据库设计中所引进的传递闭包依赖等，对这些依赖一般是按其是否具有完备的公理系统而划分为两大类，因为完备性公理系统往往具有有效的判定算法为先决条件。本对ＣＤＳ和ＦＤＳ的ｋ元完备公理系统存在问题进行了研究，证明了ＣＤＳ和ＦＤＳ不具有共同的Ｋ元完备公理系统     

Mantaining Dynamic Matrices for Fully Dynamic Transitive Closure

In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive closure. In particular, we devise a deterministic algorithm for general directed graphs that achieves O(n ²) amortized time for updates, while preserving unit worst-case cost for queries. In case of deletions only, our algorithm performs updates faster in O(n) amortized time. We observe that fully dynamic transitive closure algorithms with O(1) query time maintain explicitly the transitive closure of the input graph, in order to answer each query with exactly one lookup (on its adjacency matrix). Since an update may change as many as Ω(n ²) entries of this matrix, no better bounds are possible for this class of algorithms. This work has been partially supported by the Sixth Framework Programme of the EU under contract number 507613 (Network of Excellence “EuroNGI: Designing and Engineering of the Next Generation Internet”), and number 001907 (“DELIS: Dynamically Evolving, Large Scale Information Systems”), and by the Italian Ministry of University and Research (Project “ALGO-NEXT: Algorithms for the Next Generation Internet and Web: Methodologies, Design and Experiments”). Portions of this paper have been presented at the 41st Annual Symp. on Foundations of Computer Science, 2000.     

Efficient Transitive Closure Reasoning in a Combined Class/Part/Containment Hierarchy

Class hierarchies form the backbone of many implemented knowledge representation and reasoning systems. They are used for inheritance, classification and transitive closure reasoning. Part hierarchies are also important in artificial intelligence. Other hierarchies, e.g. containment hierarchies, have received less attention in artificial intelligence. This paper presents an architecture and an implementation of a hierarchy reasoner that integrates a class hierarchy, a part hierarchy, and a containment hierarchy into one structure. In order to make an implemented reasoner useful, it needs to operate at least at speeds comparable to human reasoning. As real-world hierarchies are always large, special techniques need to be used to achieve this. We have developed a set of parallel algorithms and a data representation called maximally reduced tree cover for that purpose. The maximally reduced tree cover is an improvement of a materialized transitive closure representation which has appeared in the literature. Our experiments with a medical vocabulary show that transitive closure reasoning for combined class/part/containment hierarchies in near constant time is possible for a fixed hardware configuration. Received 10 January 2000 / Revised 25 November 2000 / Accepted in revised form 9 February 2001     

Efficient processing of label-constraint reachability queries in large graphs

In this paper, we study a variant of reachability queries, called label-constraint reachability (LCR) queries. Specifically, given a label set S and two vertices u₁ and u₂ in a large directed graph G, we check the existence of a directed path from u₁ to u₂, where edge labels along the path are a subset of S. We propose the path-label transitive closure method to answer LCR queries. Specifically, we t4ransform an edge-labeled directed graph into an augmented DAG by replacing the maximal strongly connected components as bipartite graphs. We also propose a Dijkstra-like algorithm to compute path-label transitive closure by re-defining the “distance” of a path. Comparing with the existing solutions, we prove that our method is optimal in terms of the search space. Furthermore, we propose a simple yet effective partition-based framework (local path-label transitive closure+online traversal) to answer LCR queries in large graphs. We prove that finding the optimal graph partition to minimize query processing cost is a NP-hard problem. Therefore, we propose a sampling-based solution to find the sub-optimal partition. Moreover, we address the index maintenance issues to answer LCR queries over the dynamic graphs. Extensive experiments confirm the superiority of our method.     

传递闭包聚类中的模糊性分析

传递闭包聚类是根据其相似矩阵的传递闭包生成一个聚类图(模式空间的若干个精确划分),聚类过程的模糊性主要体现在相似矩阵上,并可以通过模糊信息熵函数度量。聚类过程中模糊性的大小是衡量聚类效果好坏的一个重要指标。降低聚类的模糊性,有利于最终的决策(指定一个精确的划分)。论文引入了交叉熵的概念,通过学习权重,极小化交叉熵,可以有效地降低聚类的模糊性。     

存储容量可扩展区块链系统的高效查询模型

区块链技术是目前计算机领域的研究热点,其实现了去中心化,并且能够安全地存储数字信息,有效降低现实经济的信任成本.提出一种区块链存储容量可扩展模型的高效查询方法——ElasticQM.此查询模型由用户层、查询层、存储层和数据层这4个模块组成.在用户层,模型将查询结果缓存,加快再次查询相同数据时的查询速度;在查询层,模型采用容量可扩展区块链模型的全局查询优化算法,增加了查询超级节点、查询验证节点和查询叶子节点这3种节点角色,提高了查询效率;在存储层,模型改进了区块链的容量可扩展模型ElasticChain的数据存储过程,实现了存储的可扩展性,并减少了占用的存储空间;在数据层,提出一种基于B-M树的区块链存储结构,并给出了B-M树的建立算法和基于B-M树的查找算法,基于B-M树的存储结构,区块链会在进行块内局部查找时提高区块链的查询速度.最后,通过在多节点不同数据量的区块链中查询的实验结果表明,ElasticQM查询方法具有高效的查询效率.     

Transitive approximation of fuzzy relations by alternating closures and openings

 In this paper, a new method is proposed for approximating a fuzzy relation on a finite universe by a min-transitive fuzzy relation that is `close' to it. The method consists of a cascade of T-transitive closure and opening operations, where the t-norm T gradually progresses from the Lukasiewicz t-norm W to the minimum operator M. The underlying T-transitive opening heuristic is particularly interesting for t-norms T that belong to the class of copulas.     

Transitive closures and orderings on soft sets

In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved.     

传感器网络中一种支持多分辨率区域查询的数据存储方法

在传感器网络中,考虑到节点的通信开销在节点总能量开销中的比重大,以及用户由粗到细分辨率的不同查询需求,有必要在传感器网络中建立支持多分辨率的数据存储机制.首先提出了一种支持多分辨率的数据压缩存储策略MDCS,节点基于MDCS在网内产生多分辨率的近似结果;其次,给出了一种基于MDCS的区域查询处理方法,根据用户给定的分辨率阈值去网内作区域查询处理,并将结果返回给用户.模拟实验表明,基于MDCS的区域查询处理方法能够高效、低能耗地支持多分辨率的区域查询操作.     

基于多重依赖关系的传递闭包研究及应用

文中通过改进Warshall-Folyd的算法,提出了一种依赖传递闭包算法和相应的动态闭包算法,其核心思想是依据依赖关系的分类和性质,定义关系矩阵和运算算子,使算法能解决选择依赖关系,并能表达直接、间接和选择三种依赖关系;同时,所提出动态算法能够运行时根据问题规模动态添加关系元素和依赖关系,解决在基本关系原则和部分关系集上求取闭包的问题。结合安全通用标准CC中关于组件间依赖关系的规定,给出了本文所提出算法的一个实际应用,表明算法取得了很好的效果。