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We consider the following four problems for a set S of k points on a plane, equippedwith the rectilinear metric and containing a set R of n disjoint rectangular obstacles (sothat distance is measured by a shortest rectilinear path avoiding obstacles in R): (a) finda closest pair of points in S, (b) find a nearest neighbor for each point in S, (c) computethe rectilinear Voronoi diagram of S, and (d) compute a rectilinear minimal spanning treeof S. We describe O((n + k) log(n + k)) time ...

Proximity problems for points on a rectilinear plane with rectangular obstacles