Finding Alternative Shortest Paths in Spatial Networks

Abstract

Shortest path query is one of the most fundamental queries in spatial network databases. There exist algorithms that can process shortest path queries in real time. However, many complex applications require more than just the calculation of a single shortest path. For example, one of the common ways to determine the importance (or price) of a vertex or an edge in spatial network is to use Vickrey pricing, which intuitively values the vertex v (or edge e ) based on how much harder for travelling from the sources to the destinations without using v (or e ). In such cases, the alternative shortest paths without using v (or e ) are required. In this article, we propose using a precomputation based approach for both single pair alternative shortest path and all pairs shortest paths processing. To compute the alternative shortest path between a source and a destination efficiently, a naïive way is to precompute and store all alternative shortest paths between every pair of vertices avoiding every possible vertex (or edge), which requires O ( n 4 ) space. Currently, the state of the art approach for reducing the storage cost is to choose a subset of the vertices as center points, and only store the single-source alternative shortest paths from those center points. Such approach has the space complexity of O ( n 2 log n ). We propose a storage scheme termed iSPQF , which utilizes shortest path quadtrees by observing the relationships between each avoiding vertex and its corresponding alternative shortest paths. We have reduced the space complexity from the naïive O ( n 4 ) (or the state of the art O ( n 4 log n )) to O (min( γ, L ) n 1.5 ) with comparable query performance of O ( K ), where K is the number of vertices in the returned paths, L is the diameter of the spatial network, and γ is a value that depends on the structure of the spatial network, which is empirically estimated to be 40 for real road networks. Experiments on real road networks have shown that the space cost of the proposed iSPQF is scalable, and both the algorithms based on iSPQF are efficient.

Finding k-shortest paths with limited overlap

“…Segment avoidance Another definition of alternative route is to compute paths that avoid certain segments of the road network. Xie et al [35] study the computation of paths that avoid specific edges of the road network and then introduce iSQPF, a spatial data structure that extends the shortest path quadtree [31], to enable the efficient computation of such paths. The concept of segment avoidance has also been studied in the context of traffic management.…”

Approximate spatio-temporal top-k publish/subscribe

“…Second, it is of interest to use POI data and geo-tagged social media data to discover significant locations/regions [13,41,[45][46][47][48]52,60]. Third, it is of interest to study integrate text data to routing problem [35,36,40,[42][43][44]56,59,66] and to study spatio-textual routing problem. Fourth, it is of interest to consider streaming data sampling and analysis, and other query types [7-9, 16, 17, 21, 23, 25, 53, 54, 57, 58, 61].…”

Data centric research at the University of Queensland

“…When spatial DBMS evolved from a highly specialized tool used by well-trained professionals to a necessity in our daily life used by everyday people from the Internet and via mobile devices, our focus moved to provide light weight access to cater for a wide range of users and devices with variable resolutions and to minimize IO costs and communication bandwidth demand. To that end we proposed multi-resolution map data access methods and spatial query processing algorithms in both the Euclidean space and some constrained spaces such as road-networks and terrain surfaces [45,9,43].…”