Prune-and-search with limited workspace

摘要

Prune-and-search is an excellent algorithmic paradigm for solving various optimization problems. We provide a general scheme for prune-and-search technique and show how to implement it in space-efficient manner. We consider both the in-place and read-only model which have several advantages compared to the traditional model of computation. Our technique can be applied to a large number of problems which accept prune-and-search. For examples, we study the following problems each of which has tremendous practical usage apart from theoretical implication:•computing the minimum enclosing circle (MEC) of a set of n points in R2, and•linear programming problems with two and three variables and n constraints. In the in-place setting, all these problems can be solved in O(n) time using O(1) extra-space. In the read-only setup, the time and extra-space complexities of the proposed algorithms for all these problems are O(npolylog(n)) and O(polylog(n)), respectively.