Path Queries Research Articles

Addressing Real-Time Demands for Robotic Path Planning Systems: A Routing Protocol Approach

Path quality and computational time have formed together a well-known trade-off problem for path planning techniques. Due to this trade-off, contributions were usually considering improving only one of the two aspects, either increasing the swiftness as in real-time robotic path planning algorithms or enhancing the path quality as in shortest path query algorithms. Producing a path planning technique that targets both aspects is a challenging problem for robotic systems. However, this paper proposes a novel path planning framework that controls the motion of robotic systems and aims to overcome this traditional trade-off challenge, by targeting both, decreasing the computational time, and improving the path quality represented by the path length and smoothness. The shortest path is obtained by minimizing a novel objective function inspired by the artificial potential field methodology. To accelerate the execution, the Particle Swarm Optimization (PSO) technique is adopted to obtain the optimal solution in a real-time hop-by-hop manner imitating the procedures performed by computer network routing protocols. Testbed experimental results have proven the effectiveness of the proposed technique and showed superior performance over other meta-heuristic optimization techniques and over classical path planning approaches such as A*, D*, and PRM.

Towards Indoor Temporal-variation aware Shortest Path Query

The recent years have witnessed the growing popularity of indoor location-based services (LBS) in practice and research. Among others, indoor shortest path query (ISPQ) is of fundamental importance for indoor LBS. However, existing works on ISPQ ignore indoor temporal variations, e.g., the open and close times associated with entities like doors and rooms. In this paper, we define a new type of query called Indoor Temporal-variation aware Shortest Path Query (ITSPQ). It returns the valid shortest path based on the up-to-date indoor topology at the query time. A set of techniques is designed to answer ITSPQ efficiently. We design a graph structure (IT-Graph) that captures indoor temporal variations. To process ITSPQ using IT-Graph, we design two algorithms that check a doors accessibility synchronously and asynchronously. Furthermore, we propose a novel index structure (IT-Index) that extends the state-of-the-art index significantly by storing dynamic door-to-door distances in a compact distance cube associated with tree nodes. When processing ITSPQ using IT-Index, we make use of the distance cube to avoid time-consuming indoor distance computation on-the-fly. We evaluate the proposed techniques using extensive experiments on synthetic and real data. The results show that our IT-Index based method is the most efficient for processing ITSPQ at a modest cost of index memory consumption.

Blocking an Evader in a Polygon by a 2-Modem Searcher

In this paper, we introduce a version of Pursuit-Evasion problem in which the pursuer is a 2-modem which pursues an unpredictable evader in a polygonal environment. A 2-modem searcher is a wireless device whose radio signal can penetrate two walls. Furthermore, a query path inside the polygon is given so that the 2-modem moves on it. We want to find out that when the 2- modem moves on this path if evaders can move from an invisible region to another one without detecting by the pursuer or not. In the other word, we want to find out if the invisible regions merge together or not.

Shortest Path Algorithm in Dynamic Restricted Area Based on Unidirectional Road Network Model.

Accurate and fast path calculation is essential for applications such as vehicle navigation systems and transportation network routing. Although many shortest path algorithms for restricted search areas have been developed in the past ten years to speed up the efficiency of path query, the performance including the practicability still needs to be improved. To settle this problem, this paper proposes a new method of calculating statistical parameters based on a unidirectional road network model that is more in line with the real world and a path planning algorithm for dynamically restricted search areas that constructs virtual boundaries at a lower confidence level. We conducted a detailed experiment on the proposed algorithm with the real road network in Zhengzhou. As the experiment shows, compared with the existing algorithms, the proposed algorithm improves the search performance significantly in the condition of optimal path under the premise of ensuring the optimal path solution.

DE-Sword: Incentivized Verifiable Tag Path Query in RFID-Enabled Supply Chain Systems

In this article, we propose Double Edged (DE)-Sword, an incentivized verifiable tag path query scheme. DE-Sword queries tag records stored across a path of participants within an RFID-enabled supply chain in a verifiable way. Different with previous works, DE-Sword works in a dishonest-data owner model in which participants are the owners of tag records and may be dishonest. DE-Sword introduces a novel double-edged reputation incentive mechanism to encourage participants to behave honestly; and couples it with cryptographic primitives to ensure query verifiability. We evaluate DE-Sword through game theory, security analysis, and performance evaluation. The game theory and security analysis shows that DE-Sword guarantees query verifiability. The evaluation results show that DE-Sword incurs low overhead in supply chain systems.

Locally optimal routes for route choice sets

Route choice is often modelled as a two-step procedure in which travellers choose their routes from small sets of promising candidates. Many methods developed to identify such choice sets rely on assumptions about the mechanisms behind the route choice and require corresponding data sets. Furthermore, existing approaches often involve considerable complexity or perform many repeated shortest path queries. This makes it difficult to apply these methods in comprehensive models with numerous origin-destination pairs. In this paper, we address these issues by developing an algorithm that efficiently identifies locally optimal routes. Such paths arise from travellers acting rationally on local scales, whereas unknown factors may affect the routes on larger scales. Though methods identifying locally optimal routes are available already, these algorithms rely on approximations and return only few, heuristically chosen paths for specific origin-destination pairs. This conflicts with the demands of route choice models, where an exhaustive search for many origins and destinations would be necessary. We therefore extend existing algorithms to return (almost) all admissible paths between a large number of origin-destination pairs. We test our algorithm and its applicability in route choice models on the road network of the Canadian province British Columbia and empirical data collected in this province.

KnowID: An Architecture for Efficient Knowledge-Driven Information and Data Access

Modern information systems require the orchestration of ontologies, conceptual data modeling techniques, and efficient data management so as to provide a means for better informed decision-making and to keep up with new requirements in organizational needs. A major question in delivering such systems, is which components to design and put together to make up the required “knowledge to data” pipeline, as each component and process has trade-offs. In this paper, we introduce a new knowledge-to-data architecture, KnowID. It pulls together both recently proposed components and we add novel transformation rules between Enhanced Entity-Relationship (EER) and the Abstract Relational Model to complete the pipeline. KnowID's main distinctive architectural features, compared to other ontology-based data access approaches, are that runtime use can avail of the closed world assumption commonly used in information systems and of full SQL augmented with path queries.

PPQ-trajectory

We present PPQ-trajectory, a spatio-temporal quantization based solution for querying large dynamic trajectory data. PPQ-trajectory includes a partition-wise predictive quantizer (PPQ) that generates an error-bounded codebook with autocorrelation and spatial proximity-based partitions. The codebook is indexed to run approximate and exact spatio-temporal queries over compressed trajectories. PPQ-trajectory includes a coordinate quadtree coding for the codebook with support for exact queries. An incremental temporal partition-based index is utilised to avoid full reconstruction of trajectories during queries. An extensive set of experimental results for spatio-temporal queries on real trajectory datasets is presented. PPQ-trajectory shows significant improvements over the alternatives with respect to several performance measures, including the accuracy of results when the summary is used directly to provide approximate query results, the spatial deviation with which spatio-temporal path queries can be answered when the summary is used as an index, and the time taken to construct the summary. Superior results on the quality of the summary and the compression ratio are also demonstrated.

Efficient Compilation of Regular Path Queries

Ad hoc code generation is a state-of-the-art processing paradigm for database execution engines. It minimizes resource consumption by generating specialized code, tailored and streamlined for the single query at hand. In this work, we apply ad hoc code generation to regular path queries (RPQs), an advanced query type in declarative graph query languages. We investigate code generation from multiple angles. We propose COAT, an embedded domain specific language (EDSL) in C++ to improve accessibility of code generation by simplifying the interaction with compiler APIs. Furthermore, we analyze and compare two back ends for COAT providing the just-in-time (JIT) compilation functionality: LLVM, a compiler framework popularly used in databases for code generation, and AsmJit, a JIT assembler with very low compilation latency. We evaluate various compilation techniques for RPQs on different synthetic graph workloads.

A divide-and-conquer algorithm for two-point L1 shortest path queries in polygonal domains

Let $P$ be a polygonal domain of $h$ holes and $n$ vertices. We study the problem of constructing a data structure that can compute a shortest path between $s$ and $t$ in $P$ under the $L_1$ metric for any two query points $s$ and $t$. To do so, a standard approach is to first find a set of $n_s$ gateways for $s$ and a set of $n_t$ gateways for $t$ such that there exist a shortest $s-t$ path containing a gateway of $s$ and a gateway of $t$, and then compute a shortest $s-t$ path using these gateways. Previous algorithms all take quadratic $O(n_s n_t)$ time to solve this problem. In this paper, we propose a divide-and-conquer technique that solves the problem in $O(n_s + n_t\log n_s)$ time. As a consequence, we construct a data structure of $O(n+(h^2 \log^3 h / \log\log h))$ size in $O(n+(h^2 \log^4 h / \log\log h))$ time such that each query can be answered in $O(\log n)$ time.

Shortest paths among transient obstacles

We present an optimal algorithm for determining a time-minimal rectilinear path among transient rectilinear obstacles. An obstacle is transient if it exists only for a specific time interval, i.e., it appears and then disappears at specific times. Given a point robot moving with bounded speed among non-intersecting transient rectilinear obstacles and a pair of points (s, d), we determine a time-minimal, obstacle-avoiding path from s to d. Our algorithm runs in $$\varTheta (n \log n)$$ time, where n is the total number of vertices in the obstacle polygons. The main challenge in solving this problem arises when the robot may be required to wait for an obstacle to disappear, before it can continue moving towards its destination. Our algorithm builds on the continuous Dijkstra paradigm, which simulates propagating a wavefront from the source point. We also present an $$O(n^2 \log n)$$ time algorithm for computing the Euclidean shortest path map among transient polygonal obstacles in the plane. This decreases the time complexity of the existing algorithm (Fujimura, in: Proceedings 1992 IEEE international conference on robotics and automation, vol 2, pp 1488–1493, 1992. https://doi.org/10.1109/ROBOT.1992.220041 ) by a factor of n. The shortest path map can be preprocessed for point location, after which a shortest path query from s to any point d can be answered in time $$O(\log n + k)$$ where, k is the number of edges in the path.

Succinct Encodings for Families of Interval Graphs

We consider the problem of designing succinct data structures for interval graphs with n vertices while supporting degree, adjacency, neighborhood and shortest path queries in optimal time. Towards showing succinctness, we first show that at least $$n\log _2{n} - 2n\log _2\log _2 n - O(n)$$ bits are necessary to represent any unlabeled interval graph G with n vertices, answering an open problem of Yang and Pippenger (Proc Am Math Soc Ser B 4(1):1–3, 2017). This is augmented by a data structure of size $$n\log _2{n} +O(n)$$ bits while supporting not only the above queries optimally but also capable of executing various combinatorial algorithms (like proper coloring, maximum independent set etc.) on interval graphs efficiently. Finally, we extend our ideas to other variants of interval graphs, for example, proper/unit interval graphs, k-improper interval graphs, and circular-arc graphs, and design succinct data structures for these graph classes as well along with supporting queries on them efficiently.

Presburger Constraints in Trees

The fully enriched µ-calculus is an expressive propositional modal logic with least and greatest fixed-points, nominals, inverse programs and graded modalities. Several fragments of this logic are known to be decidable in EXPTIME. However, the full logic is undecidable. Nevertheless, it has been recently shown that the fully enriched µ-calculus is decidable in EXPTIME when its models are finite trees. In the present work, we study the fully-enriched µ-calculus for trees extended with Presburger constraints. These constraints generalize graded modalities by restricting the number of children nodes with respect to Presburger arithmetic expressions. We show that this extension is decidable in EXPTIME. In addition, we also identify decidable extensions of regular tree languages (XML schemas) with interleaving and counting operators. This is achieved by alinear characterization in terms of the logic. Regular path queries (XPath) with Presburger constraints on children paths are also characterized. These results imply new optimal reasoning (emptiness, containment, equivalence) bounds on counting extensions of XPathqueries and XML schemas.

Presburger Constraints in Trees

The fully enriched µ-calculus is an expressive propositional modal logic with least and greatest fixed-points, nominals, inverse programs and graded modalities. Several fragments of this logic are known to be decidable in EXPTIME. However, the full logic is undecidable. Nevertheless, it has been recently shown that the fully enriched µ-calculus is decidable in EXPTIME when its models are finite trees. In the present work, we study the fully-enriched µ-calculus for trees extended with Presburger constraints. These constraints generalize graded modalities by restricting the number of children nodes with respect to Presburger arithmetic expressions. We show that this extension is decidable in EXPTIME. In addition, we also identify decidable extensions of regular tree languages (XML schemas) with interleaving and counting operators. This is achieved by alinear characterization in terms of the logic. Regular path queries (XPath) with Presburger constraints on children paths are also characterized. These results imply new optimal reasoning (emptiness, containment, equivalence) bounds on counting extensions of XPathqueries and XML schemas.

Efficient Path Query Processing Over Massive Trajectories on the Cloud

A path query aims to find trajectories passing a given sequence of connected road segments within a time period. It is very useful in many urban applications: 1) traffic modeling, 2) frequent path mining, 3) intersection coordination, and 4) traffic anomaly detection. Existing solutions for path query processing 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 from urban data mining applications. In this paper, we design and implement a cloud-based path query processing framework based on Microsoft Azure. We modify existing suffix tree structure to index trajectories using Azure Table. The proposed system consists of two main parts: 1) back-end processing , which performs pre-processing (i.e., parsing and map-matching) and index building tasks with a 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 I/O bottleneck. Extensive experiments are performed based on the real-time taxi trajectories from Guiyang City, the capital of Guizhou Province, China to confirm the system efficiency. We also demonstrate a real deployed traffic analysis system based on our query processing framework.

Shortest paths and convex hulls in 2D complexes with non-positive curvature

Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many algorithms and properties of shortest paths and convex hulls in Euclidean space fail to transfer over. We give an algorithm, using linear programming, to compute the convex hull of a set of points in a 2-dimensional CAT(0) polyhedral complex with a single vertex. We explore the use of shortest path maps to answer single-source shortest path queries in 2-dimensional CAT(0) polyhedral complexes, and we unify efficient solutions for 2-manifold and rectangular cases.

Distributed Multimodal Path Queries

Multimodal path queries over transportation networks are receiving increasing attention due to their widespread applications. A multimodal path query consists of finding multimodal journeys from source to destination in transportation networks, including unrestricted walking, driving, cycling, and schedule-based public transportation. Transportation networks are generally continent-sized. This characteristic highlights the need for parallel computing to accelerate multimodal path queries. Meanwhile, transportation networks are often fragmented and distributively stored on different machines. This situation calls for exploiting parallel computing power for these distributed systems. Therefore, in this paper, we study distributed multimodal path (DMP) queries over large transportation networks. We develop algorithms to explore parallel computation. When evaluating a DMP query Q on a distributed multimodal graph Gmult, we show that the algorithms possess the following performance guarantees, irrespective of how Gmult is fragmented and distributed: (1) each machine is visited only once; (2) the total network traffic is determined by the size of Q and the fragmentation of Gmult, independent of the size of Gmult; (3) the response time is decided by the largest fragment of Gmult; and (4) the algorithm is parallel scalable. Using real-life and synthetic data, we experimentally verify that the algorithms are scalable on large graphs.

Efficient shortest path index maintenance on dynamic road networks with theoretical guarantees

Computing the shortest path between two vertices is a fundamental problem in road networks that is applied in a wide variety of applications. To support efficient shortest path query processing, a plethora of index-based methods have been proposed in the literature, but few of them can support dynamic road networks commonly encountered in practice, as their corresponding index structures cannot be efficiently maintained when the input road network is dynamically updated. Motivated by this, we study the shortest path index maintenance problem on dynamic road networks in this paper. We adopt Contraction Hierarchies (CH) as our underlying shortest path computation method because of its outstanding overall performance in pre-processing time, space cost, and query processing time and aim to design efficient algorithms to maintain the index structure, shortcut index , of CH when the input road network is dynamically updated. To achieve this goal, we propose a shortcut-centric paradigm focusing on exploring a small number of shortcuts to maintain the shortcut index. Following this paradigm, we design an auxiliary data structure named SS-Graph and propose a shortcut weight propagation mechanism based on the SS-Graph. With them, we devise efficient algorithms to maintain the shortcut index in the streaming update and batch update scenarios with non-trivial theoretical guarantees. We experimentally evaluate our algorithms on real road networks and the results demonstrate that our approach achieves 2--3 orders of magnitude speedup compared to the state-of-the-art algorithm for the streaming update.

Group Processing of Multiple k-Farthest Neighbor Queries in Road Networks

Advances in mobile technologies and map-based applications enables users to utilize sophisticated spatial queries, including k-nearest neighbor and shortest path queries. Often, location-based servers are used to handle multiple simultaneous queries because of the popularity of map-based applications. This study focuses on the efficient processing of multiple concurrent k-farthest neighbor (kFN) queries in road networks. For a positive integer k, query point q, and set of data points P, a kFN query returns k data points farthest from the query point q. For addressing multiple concurrent spatial queries, traditional location-based servers based on one-query-at-a-time processing are unsuitable owing to high redundant computation costs. Therefore, we propose a group processing of multiple kFN (GMP) algorithm to process multiple kFN queries in road networks. The proposed GMP algorithm uses group computation to avoid the redundant computation of network distances between the query and data points. The experiments using real-world roadmaps demonstrate the proposed solution's effectiveness and efficiency.

Temporal Graph Traversals Using Reinforcement Learning With Proximal Policy Optimization

Graphs in real-world applications are dynamic both in terms of structures and inputs. Information discovery in such networks, which present dense and deeply connected patterns locally and sparsity globally can be time consuming and computationally costly. In this paper we address the shortest path query in spatio-temporal graphs which is a fundamental graph problem with numerous applications. In spatio-temporal graphs, shortest path query classical algorithms are insufficient or even flawed because information consistency can not be guaranteed between two timestamps and path recalculation is computationally costly. In this work, we address the complexity and dynamicity of the shortest path query in spatio-temporal graphs with a simple, yet effective model based on Reinforcement Learning with Proximal Policy Optimization. Our solution simplifies the problem by decomposing the spatio-temporal graph in two components: a static and a dynamic sub-graph. The static graph, known and immutable, is efficiently solved with $A^{*}$ algorithm. The sub-graphs interconnecting the static graph have unknown dynamics and we address such issue by estimating the unknown dynamic portion of the graph as a Markov Chain which correlates the observations of the agents in the environment and the path to be followed. We then derive an action policy through Proximal Policy Optimization to select the local optimal actions in the Markov Process that will lead to the shortest path, given the estimated system dynamics. We evaluate the system in a simulation environment constructed in Unity3D. In partially structured and unknown environments, with variable environment parameters we’ve obtained an efficiency 75% greater than the comparable deterministic solution.