Dynamic Three-Dimensional Linear Programming

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. 

• Type: Conference
• Year: 1991
• Where: FOCS
• Authors: David Eppstein
• Keywords: FOCS 1991, Linear Programming, Linear Programming Optimizations, Outer Recursive Decompositions, Theoretical Computer Science