New results on shortest paths in three dimensions

Joseph S.B. Mitchell*, Micha Sharir

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


We revisit the problem of computing shortest obstacle-avoiding paths among obstacles in three dimensions. We prove new hardness results, showing, e.g., that computing Euclidean shortest paths among sets of "stacked" axis-aligned rectangles is NP-complete, and that computing L 1-shortest paths among disjoint balls is NP-complete. On the positive side, we present an efficient algorithm for computing an L 1shortest path between two given points that lies on or above a given polyhedral terrain. We also give polynomial-time algorithms for some versions of stacked polygonal obstacles that are "terrain-like" and analyze the complexity of shortest path maps in the presence of parallel halfplane "walls".

Original languageEnglish
Number of pages10
StatePublished - 2004
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: 9 Jun 200411 Jun 2004


ConferenceProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
Country/TerritoryUnited States
CityBrooklyn, NY


  • Motion planning
  • NP-hardness
  • Shortest path
  • Terrain


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