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Rectilinear Shortest Paths Among Transient Obstacles

  • Anil Maheshwari
  • Arash Nouri
  • Jörg-Rüdiger Sack
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)

Abstract

This paper presents an optimal \(\varTheta (n \log n)\) algorithm for determining time-minimal rectilinear paths among n transient rectilinear obstacles. An obstacle is transient if it exists in the scene only for a specific time interval, i.e., it appears and then disappears at specific times. Given a point robot moving with bounded speed among transient rectilinear obstacles and a pair of points s, d, we determine a time-minimal, obstacle-avoiding path from s to d. The main challenge in solving this problem arises as the robot may be required to wait for an obstacle to disappear, before it can continue moving toward the destination. Our algorithm builds on the continuous Dijkstra paradigm, which simulates propagating a wavefront from the source point. We also solve a query version of this problem. For this, we build a planar subdivision with respect to a fixed source point, so that minimum arrival time to any query point can be reported in \(O(\log n)\) time, using point location for the query point in this subdivision.

Keywords

Shortest path Transient obstacles Time minimal path Time discretization Continuous dijkstra 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Anil Maheshwari
    • 1
  • Arash Nouri
    • 1
  • Jörg-Rüdiger Sack
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada

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