Computing a Median Point of a Simple Rectilinear Polygon


Let P be a simple rectilinear polygon with n vertices, endowed with rectilinear metric. Let us assign to points Xl,..., xk E P positive weights ~1, . . . , wk. The median problem consists in the computing the point minimizing the total weighted distances to the given points. We present an 0 (n + k log n ) algorithm for solving this median problem. If all weighted points are vertices of a polygon P, then the running time becomes O(n + k).

DOI: 10.1016/0020-0190(94)90100-7

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@article{Chepoi1994ComputingAM, title={Computing a Median Point of a Simple Rectilinear Polygon}, author={Victor Chepoi and Feodor F. Dragan}, journal={Oper. Res. Lett.}, year={1994}, volume={35}, pages={54-60} }