Optimal time-space tradeoff for the 2D convex-hull problem

Abstract

We revisit the read-only random-access model, in which the input array is read-only and a limited amount of workspace is allowed. Given a set of N two-dimensional points in a read-only input array and Θ(S) bits of extra workspace (where S ≥ lg N), we present an algorithm that runs in O(N 2/S + N lg S) time for constructing the convex hull formed by the given points. Following a lower bound for sorting, our algorithm is asymptotically optimal with respect to the read-only random-access model. Of independent interest, we introduce a space-efficient data structure that we call the augmented memory-adjustable navigation pile. We expect this data structure to be a useful tool when designing other space-efficient algorithms. © 2014 Springer-Verlag Berlin Heidelberg.