Output bounds for conjunctions of path queries

Path queries such as finding the shortest path in travel time from my hotel to the are heavily used in many applications of road networks. Currently, simple statistic aggregates such as the average travel time between two vertices are often used to answer path queries. However, such simple aggregates often cannot capture the uncertainty inherent in traffic. In this paper, we study how to take traffic uncertainty into account in answering path queries in road networks. To capture the uncertainty in traffic such as the travel time between two vertices, the weight of an edge is modeled as a random variable and is approximated by a set of samples. We propose three novel types of probabilistic path queries using basic probability principles: (1) a probabilistic path query like what are the paths from my hotel to the airport whose travel time is at most 30 minutes with a probability of at least 90%?; (2) a weight-threshold top-k path query like what are the top-3 paths from my hotel to the airport with the highest probabilities to take at most 30 minutes?; and (3) a probability-threshold top-k path query like what are the top-3 shortest paths from my hotel to the airport whose travel time is guaranteed by a probability of at least 90%? To evaluate probabilistic path queries efficiently, we develop three efficient probability calculation methods: an exact algorithm, a constant factor approximation method and a sampling based approach. Moreover, we devise the P* algorithm, a best-first search method based on a novel hierarchical partition tree index and three effective heuristic evaluation functions. An extensive empirical study using real road networks and synthetic data sets shows the effectiveness of the proposed path queries and the efficiency of the query evaluation methods.

With the rapid development of information technology and intelligence, there are more and more usage scenarios of graph data. Path queries have always been a hot topic of research for scholars. There are already many mature methods and ideas in the study of the path query on the plaintext graph. For the path query on graph data in the case of cloud outsourcing, it is necessary to consider both the construction of query algorithms and the protection of privacy information. The processing of graph privacy information through encryption, and then outsourcing to the cloud platform, is a common measure. The semantic‐based path query supporting multikeyword search is an extended path query method, which can improve the query function. For users, it is very troublesome to access and process the encrypted graph data. In this article, we propose a protecting‐privacy semantic‐based multikeyword path query scheme on the ciphertext graph (PSMP). Firstly, based on the principle of searchable encryption and vector operation, a secure index is constructed, and then the cloud server uses the secure index to implement path queries. This article demonstrates its security through formal analysis and verifies its effectiveness through experimental comparison and analysis. The work of this article has a certain promoting effect on the query processing and analysis of ciphertext graph data.

Given a directed graph, \(G=(V,E)\), a path query, path(u, v), returns whether there is a directed path from u to v in G, for \(u,v\in V\). Given only V, exactly learning all the edges in G using path queries is often impossible, since path queries cannot detect transitive edges. In this paper, we study the query complexity of exact learning for cases when learning G is possible using path queries. In particular, we provide efficient learning algorithms, as well as lower bounds, for multitrees and almost-trees, including butterfly networks.KeywordsGraph reconstructionExact learningDirected acyclic graphs

We introduce a representative dissimilar path (RDP) query, a novel type of path query in road networks. The k representative paths (RPs) between a source and a destination locations have k smallest costs for a feature (e.g., length, number of road intersections, or straightness). Given x features and k, an RDP query returns a set of paths for a source-destination pair such that the path set includes at least one of the k RPs for every feature, and the path set's similarity score is minimized. We formulate a novel measure to quantify the similarity of a set of paths. Considering different road features and incorporating the novel similarity measure in the computation of RDPs allow us to accommodate the human movement dynamics between two locations in an effective way. Finding the RDPs is a computational challenge because an RDP query requires computing the RPs for multiple features and then finding the RDPs from an exponential number of path combinations. We develop an efficient solution to answer RDP queries. The underlying ideas behind the efficiency of our algorithms are the refinement of the search space, finding the RPs for multiple features with a single search, and exploiting both the lower and upper bounds of the path set's similarity score while identifying the RDPs. We show the efficacy of the RDP query and the efficiency of our solution to answer the RDP query in extensive experiments using real datasets.

Efficiently processing shortest path (SP) queries over stochastic networks attracted a lot of research attention as such queries are very popular in the emerging real world applications such as Intelligent Transportation Systems and communication networks whose edge weights can be modeled as a random variable. Some pervious works aim at finding the most likely SP (the path with largest probability to be SP), and others search the least-expected-weight path. In all these works, the definitions of the shortest path query are based on simple probabilistic models which can be converted into the multi-objective optimal issues on a weighted graph. However, these simple definitions miss important information about the internal structure of the probabilistic paths and the interplay among all the uncertain paths. Thus, in this paper, we propose a new SP definition based on the possible world semantics that has been widely adopted for probabilistic data management, and develop efficient methods to find threshold-based SP path queries over an uncertain graph. Extensive experiments based on real data sets verified the effectiveness of the proposed methods.

Efficiently processing shortest path (SP) queries over stochastic networks attracted a lot of research attention as such queries are very popular in the emerging real world applications such as Intelligent Transportation Systems and communication networks whose edge weights can be modeled as a random variable. Some pervious works aim at finding the most likely SP (the path with largest probability to be SP), and others search the least-expected-weight path. In all these works, the definitions of the shortest path query are based on simple probabilistic models which can be converted into the multi-objective optimal issues on a weighted graph. Challenging problem, two algorithms, the PEEDR and the CPGS clustering algorithm. Reliable clusters are those which are not likely to be disconnected in the context of different instantiations of the uncertain graph. we provide a generalized reliability measurement from two basic intuitions (purity and size balance) to overcome the challenges from standard reliability criterion, and develop a novel k-means algorithm to solve the uncertain clustering problem

Explaining results of path queries on graphs: Single-path results for context-free path queries

A path query aims to find the trajectories that pass a given sequence of connected road segments within a time period. It is very useful in many urban applications, e.g., 1) traffic modeling, 2) frequent path mining, and 3) traffic anomaly detection. Existing solutions for path query are implemented based on single machines, which are not efficient for the following tasks: 1) indexing large-scale historical data; 2) handling real-time trajectory updates; and 3) processing concurrent path queries. In this paper, we design and implement a cloud-based path query processing framework based on Microsoft Azure. We modify the suffix tree structure to index the trajectories using Azure Table. The proposed system consists of two main parts: 1) backend processing, which performs the pre-processing and suffix index building with distributed computing platform (i.e., Storm) used to efficiently handle massive real-time trajectory updates; and 2) query processing, which answers path queries using Azure Storm to improve efficiency and overcome the I/O bottleneck. We evaluate the performance of our proposed system based on a real taxi dataset from Guiyang, China.

Due to the popularity of Spatial Databases, many search engine providers have started to expand their text searching capability to include geographical information. Because of this reason, many new queries on spatial objects affiliated with textual information, known as the Spatial Keyword Queries, have taken significant research interest in the past years. Unfortunately, most of existing works on Spatial Keyword Queries only focus on objects retrieval. There is barely any work on route planning queries, even though route planning is often needed in our daily life. In this research, we propose the Best Path Query, which we find the best optimum route from two different spatial locations that visits or avoids the objects that are specified by the textual data given by the user. We show that Best Path Query is an NP-Hard problem. We propose an efficient indexing technique, namely IG-Tree, and three different algorithms with different trade-offs to process the Best Path Queries on Road Networks. Our extensive experimental study demonstrates the efficiency and accuracy of our proposed approach.

With the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs, e.g., travel time, in a road network. The current paradigm for doing so is edge-centric: it represents a road network as a weighted graph and splits trajectories into small fragments that fit the underlying edges to assign time-varying and uncertain weights to edges. It then applies path finding algorithms to the resulting, weighted graph. We propose a new PAth-CEntric paradigm, PACE, that targets more accurate and more efficient path cost estimation and path finding. By assigning weights to paths, PACE avoids splitting trajectories into small fragments. We solve two fundamental problems to establish the PACE paradigm: (i) how to compute accurately the travel cost distribution of a path and (ii) how to conduct path finding for a source–destination pair. To solve the first problem, given a departure time and a query path, we show how to select an optimal set of paths that cover the query path and such that the weights of the paths enable the most accurate joint cost distribution estimation for the query path. The joint cost distribution models well the travel cost dependencies among the edges in the query path, which in turn enables accurate estimation of the cost distribution of the query path. We solve the second problem by showing that the resulting path cost distribution estimation method satisfies an incremental property that enables the method to be integrated seamlessly into existing stochastic path finding algorithms. Further, we propose a new stochastic path finding algorithm that fully explores the improved accuracy and efficiency provided by PACE. Empirical studies with trajectory data from two different cities offer insight into the design properties of the PACE paradigm and offer evidence that PACE is accurate, efficient, and effective in real-world settings.

formula omitted]: A distributed engine for scalable path queries over temporal property graphs

We present a randomized algorithm for reconstructing directed rooted trees of n nodes and node degree at most d, by asking at most $\mathcal{O}(dn \log^{2}\,n) {path queries}$. Each path query takes as input an origin node and a target node, and answers whether there is a directed path from the origin to the target. Regarding lower bounds, we show that any randomized algorithm requires at least $\Omega (n \log n)$ queries, while any deterministic algorithm requires at least $\Omega (dn)$ queries. Additionally, we present a $\mathcal{O}(dn \log^{3}\,n)$ randomized algorithm for noisy queries, and a $\mathcal{O}(dn \log^{2}\,n)$ randomized algorithm for additive queries on weighted trees.

In this paper, we consider the problem of reconstructing a directed graph using path queries. In the query model of learning, a graph is hidden from the learner, and the learner can access information about it with path queries. For a source and destination node, a path query returns whether there is a directed path from the source to the destination node in the hidden graph. We first give bounds for learning graphs on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> vertices and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> strongly connected components. We then study the case of bounded degree directed trees and give new algorithms for learning “almost-trees” - directed trees to which extra edges have been added. We also give some lower bound constructions justifying our approach.

A $k$-path query on a graph consists of computing $k$ vertex-disjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing $k$-path queries, with $k \leq 3$, in a graph $G$ with $n$ vertices. We denote with $\ell$ the total length of the paths reported. For $k \leq 3$, we present an optimal data structure for $G$ that uses $O(n)$ space and executes $k$-path queries in output-sensitive $O(\ell)$ time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar ($st$) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.

Optimizing path query performance: graph clustering strategies