求解区间图K-连接最短路径问题的在线算法

针对含有n个区间的区间图K-连接最短路径(K-SP)问题,提出一种求解区间图K-SP问题的在线算法。分析区间图及其最短路径问题的特有性质,利用改进的动态规划算法和贪心算法,优化在线算法的时间复杂度。理论分析结果表明,该算法的时间复杂度为O(nK+nlgn),与目前已知最优的离线算法复杂度相同。     

求解多段图问题的并行动态规划算法

多段图问题是一类特殊的单源最短路径问题。在串行动态规划算法的两种实现方法的基础上,根据图中顶点的编号,提出两种在集群环境下进行任务分割的并行化求解方法,并使用MPI进行实现。实验结果表明,所提出的算法具有较高的加速比和较低的通信复杂度、时间复杂度。算法不限于某种结构的集群,通用性强。     

高效的多关键词匹配最优路径查询算法KSRG

为改进基于关键词的最优路径查询算法,在大规模图以及多查询关键词下复杂度过高与可扩展性不足的缺陷,依据查询关键词序列构建候选路径的策略提出一种高效查询算法。该算法在路径构建过程中优先满足查询关键词的全包含条件,以关键词引导下的路径拓展替代盲目的邻边拓展,从而高效地构建候选路径;通过变量缩放与无效路径裁剪,将问题求解复杂度由阶乘级转化为多项式级,进一步降低算法复杂度,提升可扩展性。通过四组图数据集下的实验,验证了算法在查询效率与可扩展性上的提升。     

道路转向延迟的动态对偶图模型

传统的道路转向延迟对偶图表达法缺乏对交通网络时间依赖特性的考虑,不适合动态路径规划问题的求解。本文将时间因素引入到对偶图中,发展了一种动态对偶图模型,将交通路网表达为动态对偶网络,并为之定义了FIFO(先进先出）条件,推导了满足FIFO条件的动态行程计算方法,设计了时间依赖的标号设定最短路径算法。实验结果表明,利用该对偶图模型和动态对偶网络,能有效表达路网转向延迟,在以出行时间为标准的动态路径规划中,基于动态对偶网络的路径规划结果可节省约16%的出行时间。     

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。     

基于图的适应性多连接查询优化算法

提出一种基于图的适应性多连接查询优化算法,分析关系结果集到达时间和结果集大小之间的关系,借鉴适应性查询优化的动态调整思想,对基于图的多连接查询进行改进。仿真实验结果表明,该算法在最好情况下的时间复杂度为O（n）,且能有效提高查询效率。     

基于参考节点嵌入的图可达性查询

针对k步可达性查询算法无法解决带距离约束的图可达性查询问题,提出基于参考节点嵌入的图可达性查询算法。首先,从所有节点中选出极少数有代表性的全局参考节点,预先计算所有节点与全局参考节点之间的最短路径距离;然后,采用最短路径树和范围最小值查询技术求得局部参考节点;接着,利用三角不等式关系得到查询点对距离范围;最后,根据查询条件中的距离值与查询点对距离范围上、下限值的大小关系,可快速得出可达性结论。针对社会关系网络和公路网络数据,将所提算法与Dijkstra算法、K-Reach算法进行实验对比测试。相较于K-Reach算法,其索引建立时间小4个数量级,其索引规模小2个数量级;相较于Dijkstra算法,在公路网络和社会关系网络中,直接得出可达性结论的比例分别为92%和78.6%,其查询时间大大缩短,分别降低了95.5%和92%。实验结果表明：所提算法能够通过使用较小的索引开销,实现在线查询计算复杂度的降低,可很好地解决既适用于有权图又适用于无权图带距离约束的可达性查询问题。     

基于树分解结构的Top-k最短路径查询算法

基于树分解原理及性质,本文运用启发式树分解方法将图转换为树结构,并对分解树进行预处理,在这些预存储的索引信息中查询Top-k最短路径。将树分解索引结构应用到Yen算法,通过解决树分解结构上的限制性路径查询,即Top-1最短路径查询,依次循环求解出Top-k最短路径查询。本算法并没有改变Yen算法最坏情况下的时间复杂度,而是通过分解树上的索引信息在分解树上递归查找,快速查找出最短路径。实验结果表明,基于树分解结构的Top-k最短路径查询算法比Yen算法的查询效率高,且存储索引信息在可接受范围内。     

利用动态规划模型优化天然气产销调度问题

在不确定条件下,如何优化天然气产销调度使得产销平衡,是天然气公司急待解决的问题.天然气的购买和销售是一个多阶段动态过程,所以将动态规划理论应用其中,建立以天然气公司最大收益为目标的动态规划模型,并进行时间复杂度分析.结果表明,动态规划算法能从时间与空间角度实现天然气的合理调度;与线性求解过程相比,动态规划算法对具有最优解的实际问题的求解更加灵活,且计算量小,结果更可靠,为天然气产销优化调度提供了新的解决方法.     

无限制二维下料问题的改进动态规划算法

本文给出了一种求解无限制板材下料问题的动态规划解法，对该算法的计算复杂度 进行了分析．并针对算法的特点提出了改进方案．通过理论分析得到改进方案的适用范围， 并描述了这一改进动态规划算法的应用前景．数值实验表明，该算法可以缩简传统动态规划 算法的计算时间和空间，同时得到解的最优值．     

非稠密数据域的不等式合取查询

1988年Klug给出了第一个稠密域上的不等式合取查询包含问题的算法,但该方法不适用于非稠密域.本文解决非稠密域上的不等式合取查询的包含问题.     

基于ＳＱＬ的ＸＭＬ查询的有效实现

讨论了关系数据库中利用ＳＱＬ语句实现ＸＭＬ查询的问题,首先提出了一个利用映射信息（映射图）将带正则路径表达式的ＸＭＬ查询重写为一组简单路径查询的算法,该过程中的一个关键问题的Ｋleene表达式不能直接利用映射图重写,为此,提出了利用路径实例的统计信息来扩展Ｋleene表达式的算法,然后,进一步描述了将简单路径表达式查询重写为ＳＱＬ查询的方法,这些算法在ＸＭＬ－关系系统原型ＶＸＭＬＲ中实现,初步性能研究表明提出了方法是有效的。     

Containment of Conjunctive Queries on Annotated Relations

We study containment and equivalence of (unions of) conjunctive queries on relations annotated with elements of a commutative semiring. Such relations and the semantics of positive relational queries on them were introduced in a recent paper as a generalization of set semantics, bag semantics, incomplete databases, and databases annotated with various kinds of provenance information. We obtain positive decidability results and complexity characterizations for databases with lineage, why-provenance, and provenance polynomial annotations, for both conjunctive queries and unions of conjunctive queries. At least one of these results is surprising given that provenance polynomial annotations seem “more expressive” than bag semantics and under the latter, containment of unions of conjunctive queries is known to be undecidable. The decision procedures rely on interesting variations on the notion of containment mappings. We also show that for any positive semiring (a very large class) and conjunctive queries without self-joins, equivalence is the same as isomorphism.     

On the equivalence and rewriting of aggregate queries

We introduce a first-order language with real polynomial arithmetic and aggregation operators (count, iterated sum and multiply), which is well suited for the definition of aggregate queries involving complex statistical functions. It offers a good trade-off between expressive power and complexity, with a tractable data complexity. Interestingly, some fundamental properties of first-order with real arithmetic are preserved in the presence of aggregates. In particular, there is an effective quantifier elimination for formulae with aggregation. We then consider the problem of querying data that has already been aggregated in aggregate views, and focus on queries with an aggregation over a conjunctive query (namely single-block aggregate group-by queries without having clause). Our main conceptual contribution is the introduction of a new equivalence relation among conjunctive queries, the isomorphism modulo a product. We prove that the equivalence of aggregate queries such as for instance averages reduces to it. Deciding if two queries are isomorphic modulo a product is shown to be NP-complete. We then analyze the equivalence problem in the case of aggregate conjunctive queries with comparisons. We introduce the concept of cross isomorphic linear expansions, which generalizes isomorphim modulo a product, and we show that equivalence reduces to it and that it can be decided in PSPACE. Finally, we show that the problem of complete rewriting of count queries using count views is NP-complete, and we introduce new rewriting techniques based on the isomorphism modulo a product. to recover the values of counts by complex arithmetical computation from the views.Received: 10 July 2003, Revised: 25 April 2004, Published online: 8 June 2004     

模糊描述逻辑知识库查询蕴涵的判定方法

大规模领域本体的快速发展对语义Web领域的数据访问提出了更高的要求,而基本的本体推理服务已不能满足数据密集型应用中处理复杂查询(主要是合取查询)的迫切需要.为此,大量的研究工作集中在本体和描述逻辑知识库合取查询算法的设计实现上,并开发出了很多知识库存储和查询的实用工具.近来模糊本体和模糊描述逻辑的研究,特别是它们在处理语义Web中模糊信息方面,得到了广泛关注.文中重点研究了模糊SH这一族极富表达能力的描述逻辑知识库的合取查询问题,提出了相应的基于推演表的算法,证明了算法对于f-SHOIQ的真子逻辑的可靠性、完备性和可终止性.证明了算法对于f-SHOIQ是可靠的,并分析了导致算法不可终止的原因.对于该问题的数据复杂度,证明了当查询中不存在传递角色时其严格的CONP上限.对于联合复杂度,汪明了算法关于知识库和查询大小的CO3NEXPTIME时间复杂度上限.     

一种基于脉冲耦合神经网络的最短路径算法

提出了一种基于脉冲耦合神经网(Pulse—Coupled Neural Network，PCNN)的最短路径算法。通过对PCNN做很小的改变，该算法不但具有和Hopfield神经网络相同的并行处理特性，适用于求解大规模实时问题，而且还能一次求出源点到其它所有目的点的最短路径．根据PCNN的模型和运算规则，本文证明了该方法的正确性并分析了其复杂度．文中还将该算法运用于通信网络的路由选择．     

The Quantum Setting with Randomized Queries for Continuous Problems

The standard setting of quantum computation for continuous problems uses deterministic queries and the only source of randomness for quantum algorithms is through measurement. Without loss of generality we may consider quantum algorithms which use only one measurement. This setting is related to the worst case setting on a classical computer in the sense that the number of qubits needed to solve a continuous problem must be at least equal to the logarithm of the worst case information complexity of this problem. Since the number of qubits must be finite, we cannot solve continuous problems on a quantum computer with infinite worst case information complexity. This can even happen for continuous problems with small randomized complexity on a classical computer. A simple example is integration of bounded continuous functions. To overcome this bad property that limits the power of quantum computation for continuous problems, we study the quantum setting in which randomized queries are allowed. This type of query is used in Shor’s algorithm. The quantum setting with randomized queries is related to the randomized classical setting in the sense that the number of qubits needed to solve a continuous problem must be at least equal to the logarithm of the randomized information complexity of this problem. Hence, there is also a limit to the power of the quantum setting with randomized queries since we cannot solve continuous problems with infinite randomized information complexity. An example is approximation of bounded continuous functions. We study the quantum setting with randomized queries for a number of problems in terms of the query and qubit complexities defined as the minimal number of queries/qubits needed to solve the problem to within ɛ by a quantum algorithm. We prove that for path integration we have an exponential improvement for the qubit complexity over the quantum setting with deterministic queries.     

The trichotomy of HAVING queries on a probabilistic database

We study the evaluation of positive conjunctive queries with Boolean aggregate tests (similar to HAVING in SQL) on probabilistic databases. More precisely, we study conjunctive queries with predicate aggregates on probabilistic databases where the aggregation function is one of MIN, MAX, EXISTS, COUNT, SUM, AVG, or COUNT(DISTINCT) and the comparison function is one of =, ≠,≥,>,≤, or <. The complexity of evaluating a HAVING query depends on the aggregation function, α, and the comparison function, θ. In this paper, we establish a set of trichotomy results for conjunctive queries with HAVING predicates parametrized by (α, θ). For such queries (without self-joins), one of the following three statements is true: (1) the exact evaluation problem has P{\mathcal P} -time data complexity. In this case, we call the query safe. (2) The exact evaluation problem is \sharpP{{\sharp{\mathcal P}}} -hard, but the approximate evaluation problem has (randomized) P{{\mathcal P}} -time data complexity. More precisely, there exists an FPTRAS for the query. In this case, we call the query apx-safe. (3) The exact evaluation problem is \sharpP{{\sharp{\mathcal P}}} -hard, and the approximate evaluation problem is also hard. We call these queries hazardous. The precise definition of each class depends on the aggregate considered and the comparison function. Thus, we have queries that are (MAX,≥ )-safe, (COUNT,≤ )-apx-safe, (SUM,=)-hazardous, etc. Our trichotomy result is a significant extension of a previous dichotomy result for Boolean conjunctive queries into safe and not safe. For each of the three classes we present novel techniques. For safe queries, we describe an evaluation algorithm that uses random variables over semirings. For apx-safe queries, we describe an FPTRAS that relies on a novel algorithm for generating a random possible world satisfying a given condition. Finally, for hazardous queries we give novel proofs of hardness of approximation. The results for safe queries were previously announced (in Ré, C., Suciu, D. Efficient evaluation of. In: DBPL, pp. 186–200, 2007), but all other results are new.     

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.