A fast planar partition algorithm, I
Journal of Symbolic Computation
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
SIAM Journal on Computing
Farthest neighbors and center points in the presence of rectngular obstacles
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Voronoi Diagram for services neighboring a highway
Information Processing Letters
Proceedings of the twenty-second annual symposium on Computational geometry
The geodesic farthest-site Voronoi diagram in a polygonal domain with holes
Proceedings of the twenty-fifth annual symposium on Computational geometry
Farthest-polygon Voronoi diagrams
Computational Geometry: Theory and Applications
Shortest paths and voronoi diagrams with transportation networks under general distances
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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Given a set of roads in the plane with assigned speed, a traveler is assumed to move at the specified speed along each road, and at unit speed out of the roads. We are interested in the minimum travel time when we travel from one point in the plane to another, which defines a travel time metric. We study the farthest Voronoi diagram under this travel time metric, providing first nontrivial bounds on its combinatorial and computational complexity. Our approach is based on structural observations and recently known algorithmic technique. In particular, we show that if we are given a set of m isothetic roads with equal speed, then the diagram of n sites on the L1 plane has Θ(nm) complexity and can be computed in O(nmlog3(n+m)) time in the worst case.