Dynamic Three-Dimensional Linear Programming (1992) [33 citations — 4 self]
by
David Eppstein
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@MISC{Eppstein92dynamicthree-dimensional,
author = {David Eppstein},
title = {Dynamic Three-Dimensional Linear Programming},
year = {1992}
}
author = {David Eppstein},
title = {Dynamic Three-Dimensional Linear Programming},
year = {1992}
}
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Abstract:
We perform linear programming optimizations on the intersection of k polyhedra in R³, represented by their outer recursive decompositions, in expected time O(k log k log n + √k log k log³ n). We use this result to derive efficient algorithms for dynamic linear programming problems in which constraints are inserted and deleted, and queries must optimize specified objective functions. As an application, we describe an improved solution to the planar 2-center and 2-median problems.
