Scalable shortest paths browsing on land surface

Abstract

The growing popularity of online Earth visualization tools and geo-realistic games and the availability of high resolution terrain data have motivated a new class of queries to the interests of the GIS and spatial database community: spatial queries (e.g., kNN) over land surface. However, the fundamental challenges that restrict the applicability of these studies to real world applications are the prohibitive time complexity and storage overhead to precompute the shortest surface paths. In this paper, for the first time, we propose an approximate solution to address both challenges and allow browsing the shortest surface paths in O() time, where N is the size of the terrain. With this method, the time and space requirements for an exhaustive all-pair pre-computation have been reduced from O(N 3) to O(N 1.5) and O(N) respectively. The substantial savings in both time and storage are gained by taking advantage of the fact that the O(N 2) surface paths only deviate from approximate straight lines at O() points, termed rough vertices. As a result, we propose a linear time shortest surface path computation algorithm between two arbitrary vertices and a linear size storage structure, which captures all the shortest surface paths between any pair of vertices. We experimentally verified the applicability and scalability of the proposed methods with large real world and synthetic data sets and showed that accuracy higher than 97% can be obtained in most cases.

The Implicit Path Cost Optimization in Dijkstra Algorithm Using Hash Map Data Structure

“…It concerns with finding the shortest path between two nodes, or between a node as a source to all other nodes, depending on the weights of the edges that link these nodes [8]. The graph theory and shortest path are used widely especially in the practical applications of various fields, the most important are roads, transport networks and geographic information systems [9,10,11,12].…”

“…Based on the rapid development and handling of the huge amount of road networks data and their development methods, researchers try to improve the previous algorithms or develop their own [4,7,9,10,11,12]. They are also exploring more various ways and methods to get the lowest cost of path into a large number of nodes and speeding up their search process.…”

An Effect of Using A Storage Medium in Dijkstra Algorithm Performance for Ideal Implicit Path Cost

“…It concerns with finding the shortest path between two nodes, or between a node as a source to all other nodes, depending on the weights of the edges that link these nodes [8]. The graph theory and shortest path are used widely especially in the practical applications of various fields such as mapping transportation, electrical engineering and computer networks [9,10,11,12].…”

“…In the last decade, the number of the rapid development and handling of the huge amount of road networks data and their development methods have been increased, researchers try to improve the previous algorithms or develop their own in order to find out the typical shortest paths [4,7,9,10,11,12]. They are also exploring more various ways and methods to get the lowest cost of path into a large number of nodes and speeding up their search process.…”