Deterministic Algorithms for 2-d Convex Programming and 3-d Online Linear Programming
Timothy M. Chan · Journal of Algorithms · 1998
We present a deterministic algorithm for solving two-dimensional convex programs with a linear objective function. The algorithm requiresO(k log k) primitive operations forkconstraints; if a feasible point is given, the bound reduces toO(k log k/log log k). As a consequence, we can decide whetherkconvexn-gons in the plane have a common intersection inO(k log n min{log k, log log n}) worst-case time. Furthermore, we can solve the three-dimensional online programming problem ino(log3 n) worst-case time per operation.