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Register a new userShortest Path and Distance Queries on Road Networks: An Experimental Evaluation
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Added by
Xiaokui Xiao
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be divided into two categories: spatial-coherence-based methods and vertex-importance-based approaches. The two categories of techniques, however, have not been compared systematically under the same experimental framework, as they were developed from two independent lines of research that do not refer to each other. This renders it difficult for a practitioner to decide which technique should be adopted for a specific application. Furthermore, the experimental evaluation of the existing techniques, as presented in previous work, falls short in several aspects. Some methods were tested only on small road networks with up to one hundred thousand vertices; some approaches were evaluated using distance queries (instead of shortest path queries), namely, queries that ask only for the length of the shortest path; a state-of-the-art technique was examined based on a faulty implementation that led to incorrect query results. To address the above issues, this paper presents a comprehensive comparison of the most advanced spatial-coherence-based and vertex-importance-based approaches. Using a variety of real road networks with up to twenty million vertices, we evaluated each technique in terms of its preprocessing time, space consumption, and query efficiency (for both shortest path and distance queries). Our experimental results reveal the characteristics of different techniques, based on which we provide guidelines on selecting appropriate methods for various scenarios.
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Given two locations $s$ and $t$ in a road network, a distance query returns the minimum network distance from $s$ to $t$, while a shortest path query computes the actual route that achieves the minimum distance. These two types of queries find important applications in practice, and a plethora of solutions have been proposed in past few decades. The existing solutions, however, are optimized for either practical or asymptotic performance, but not both. In particular, the techniques with enhanced practical efficiency are mostly heuristic-based, and they offer unattractive worst-case guarantees in terms of space and time. On the other hand, the methods that are worst-case efficient often entail prohibitive preprocessing or space overheads, which render them inapplicable for the large road networks (with millions of nodes) commonly used in modern map applications. This paper presents {em Arterial Hierarchy (AH)}, an index structure that narrows the gap between theory and practice in answering shortest path and distance queries on road networks. On the theoretical side, we show that, under a realistic assumption, AH answers any distance query in $tilde{O}(log r)$ time, where $r = d_{max}/d_{min}$, and $d_{max}$ (resp. $d_{min}$) is the largest (resp. smallest) $L_infty$ distance between any two nodes in the road network. In addition, any shortest path query can be answered in $tilde{O}(k + log r)$ time, where $k$ is the number of nodes on the shortest path. On the practical side, we experimentally evaluate AH on a large set of real road networks with up to twenty million nodes, and we demonstrate that (i) AH outperforms the state of the art in terms of query time, and (ii) its space and pre-computation overheads are moderate.
Finding the shortest paths in road network is an important query in our life nowadays, and various index structures are constructed to speed up the query answering. However, these indexes can hardly work in real-life scenario because the traffic condition changes dynamically, which makes the pathfinding slower than in the static environment. In order to speed up path query answering in the dynamic road network, we propose a framework to support these indexes. Firstly, we view the dynamic graph as a series of static snapshots. After that, we propose two kinds of methods to select the typical snapshots. The first kind is time-based and it only considers the temporal information. The second category is the graph representation-based, which considers more insights: edge-based that captures the road continuity, and vertex-based that reflects the region traffic fluctuation. Finally, we propose the snapshot matching to find the most similar typical snapshot for the current traffic condition and use its index to answer the query directly. Extensive experiments on real-life road network and traffic conditions validate the effectiveness of our approach.
Traditional route planning and $k$ nearest neighbors queries only consider distance or travel time and ignore road safety altogether. However, many travellers prefer to avoid risky or unpleasant road conditions such as roads with high crime rates (e.g., robberies, kidnapping, riots etc.) and bumpy roads. To facilitate safe travel, we introduce a novel query for road networks called the $k$ safest nearby neighbors ($k$SNN) query. Given a query location $v_l$, a distance constraint $d_c$ and a point of interest $p_i$, we define the safest path from $v_l$ to $p_i$ as the path with the highest path safety score among all the paths from $v_l$ to $p_i$ with length less than $d_c$. The path safety score is computed considering the road safety of each road segment on the path. Given a query location $v_l$, a distance constraint $d_c$ and a set of POIs $P$, a $k$SNN query returns $k$ POIs with the $k$ highest path safety scores in $P$ along with their respective safest paths from the query location. We develop two novel indexing structures called $Ct$-tree and a safety score based Voronoi diagram (SNVD). We propose two efficient query processing algorithms each exploiting one of the proposed indexes to effectively refine the search space using the properties of the index. Our extensive experimental study on real datasets demonstrates that our solution is on average an order of magnitude faster than the baselines.
Graph data models have recently become popular owing to their applications, e.g., in social networks and the semantic web. Typical navigational query languages over graph databases - such as Conjunctive Regular Path Queries (CRPQs) - cannot express relevant properties of the interaction between the underlying data and the topology. Two languages have been recently proposed to overcome this problem: walk logic (WL) and regular expressions with memory (REM). In this paper, we begin by investigating fundamental properties of WL and REM, i.e., complexity of evaluation problems and expressive power. We first show that the data complexity of WL is nonelementary, which rules out its practicality. On the other hand, while REM has low data complexity, we point out that many natural data/topology properties of graphs expressible in WL cannot be expressed in REM. To this end, we propose register logic, an extension of REM, which we show to be able to express many natural graph properties expressible in WL, while at the same time preserving the elementariness of data complexity of REMs. It is also incomparable to WL in terms of expressive power.
The determination of time-dependent collision-free shortest paths has received a fair amount of attention. Here, we study the problem of computing a time-dependent shortest path among growing discs which has been previously studied for the instance where the departure times are fixed. We address a more general setting: For two given points $s$ and $d$, we wish to determine the function $mathcal{A}(t)$ which is the minimum arrival time at $d$ for any departure time $t$ at $s$. We present a $(1+epsilon)$-approximation algorithm for computing $mathcal{A}(t)$. As part of preprocessing, we execute $O({1 over epsilon} log({mathcal{V}_{r} over mathcal{V}_{c}}))$ shortest path computations for fixed departure times, where $mathcal{V}_{r}$ is the maximum speed of the robot and $mathcal{V}_{c}$ is the minimum growth rate of the discs. For any query departure time $t geq 0$ from $s$, we can approximate the minimum arrival time at the destination in $O(log ({1 over epsilon}) + loglog({mathcal{V}_{r} over mathcal{V}_{c}}))$ time, within a factor of $1+epsilon$ of optimal. Since we treat the shortest path computations as black-box functions, for different settings of growing discs, we can plug-in different shortest path algorithms. Thus, the exact time complexity of our algorithm is determined by the running time of the shortest path computations.
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