Convex Hull and Linear Programming in Read-only Setup with Limited Work-space

Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-andsearch technique can be implemented where the objects are given in read-only memory. As examples we consider convex-hull in 2D, and linear programming in 2D and 3D. For the convex-hull problem, designing subquadratic algorithm in a read-only setup with sub-linear space is an open problem for a long time. We first propose a simple algorithm for this problem that runs in O(n 3 2 +ǫ) time and O(n 1 2 ) space. Next, we consider a restricted version of the problem where the points in P are given in sorted order with respect to their x-coordinates in a read-only array. For the linear programming problems, the constraints are given in the read-only array. The last three algorithms use prune-and-search, and their time and extra work-space complexities are O(n) and O(log n) respectively, where ǫ is a small constant satisfying √ log log n logn < ǫ < 1.