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

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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.

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Notes

  1. https://www.mapbox.com/blog/nyc-buildings-openstreetmap/.

  2. http://www.openstreetmap.org/.

  3. We do a best-first traversal on the spatial network, and hence, only a limited number of points are tested.

  4. http://www.sl3sl.com/vb/showthread.php?t=7032.

  5. http://metro.teczno.com/#london.

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Authors and Affiliations

  1. University of Melbourne, Melbourne, Australia

    Saad Aljubayrin, Jianzhong Qi, Rui Zhang & Yuan Li

  2. Aalborg University, Aalborg, Denmark

    Christian S. Jensen

  3. Latrobe University, Melbourne, Australia

    Zhen He

Authors
  1. Saad Aljubayrin
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  2. Jianzhong Qi
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  3. Christian S. Jensen
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  4. Rui Zhang
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  5. Zhen He
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  6. Yuan Li
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Correspondence to Rui Zhang.

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Aljubayrin, S., Qi, J., Jensen, C.S. et al. Finding lowest-cost paths in settings with safe and preferred zones. The VLDB Journal 26, 373–397 (2017). https://doi.org/10.1007/s00778-017-0455-8

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  • DOI: https://doi.org/10.1007/s00778-017-0455-8

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