Finding lowest-cost paths in settings with safe and preferred zones

Finding lowest-cost paths in settings with safe and preferred zones We define and study Euclidean and spatial network variants of a new path finding problem: given a set of safe or preferred zones with zero or low cost, find paths that minimize the cost of travel from an origin to a destination. In this problem, the entire space is passable, with preference given to safe or preferred zones. Existing algorithms for problems that involve unsafe regions to be avoided strictly are not effective for this new problem. To solve the Euclidean variant, we devise a transformation of the continuous data space with safe zones into a discrete graph upon which shortest path algorithms apply. A naive transformation yields a large graph that is expensive to search. In contrast, our transformation exploits properties of hyperbolas in Euclidean space to safely eliminate graph edges, thus improving performance without affecting correctness. To solve the spatial network variant, we propose a different graph-to-graph transformation that identifies critical points that serve the same purpose as do the hyperbolas, thus also avoiding the extraneous edges. Having solved the problem for safe zones with zero costs, we extend the transformations to the weighted version of the problem, where travel in preferred zones has nonzero costs. Experiments on both real and synthetic data show that our approaches outperform baseline approaches by more than an order of magnitude in graph construction time, storage space, and query response time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The VLDB Journal Springer Journals

Finding lowest-cost paths in settings with safe and preferred zones

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Computer Science; Database Management
ISSN
1066-8888
eISSN
0949-877X
D.O.I.
10.1007/s00778-017-0455-8
Publisher site
See Article on Publisher Site

Abstract

We define and study Euclidean and spatial network variants of a new path finding problem: given a set of safe or preferred zones with zero or low cost, find paths that minimize the cost of travel from an origin to a destination. In this problem, the entire space is passable, with preference given to safe or preferred zones. Existing algorithms for problems that involve unsafe regions to be avoided strictly are not effective for this new problem. To solve the Euclidean variant, we devise a transformation of the continuous data space with safe zones into a discrete graph upon which shortest path algorithms apply. A naive transformation yields a large graph that is expensive to search. In contrast, our transformation exploits properties of hyperbolas in Euclidean space to safely eliminate graph edges, thus improving performance without affecting correctness. To solve the spatial network variant, we propose a different graph-to-graph transformation that identifies critical points that serve the same purpose as do the hyperbolas, thus also avoiding the extraneous edges. Having solved the problem for safe zones with zero costs, we extend the transformations to the weighted version of the problem, where travel in preferred zones has nonzero costs. Experiments on both real and synthetic data show that our approaches outperform baseline approaches by more than an order of magnitude in graph construction time, storage space, and query response time.

Journal

The VLDB JournalSpringer Journals

Published: Jan 30, 2017

References

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