Space-time trade-offs for stack-based algorithms

In memory-constrained algorithms, access to the input is restricted to be read-only, and the number of extra variables that the algorithm can use is bounded. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose main memory consumption takes the form of a stack into memory-constrained algorithms. Given an algorithm A that runs in O(n) time using a stack of length Θ(n), we can modify it so that it runs in O(n2 logn/2s) time using a workspace of O(s) variables (for any s ∈ o(logn)) or O(n1+1 / log p) time using O(p logp n) variables (for any 2 ≤ p ≤ n). We also show how the technique can be applied to solve various geometric problems, namely computing the convex hull of a simple polygon, a triangulation of a monotone polygon, the shortest path between two points inside a monotone polygon, a 1-dimensional pyramid approximation of a 1-dimensional vector, and the visibility profile of a point inside a simple polygon. Our approach improves or matches up to a O(logn) factor the running time of the best-known results for these problems in constant-workspace models (when they exist), and gives a trade-off between the size of the workspace and running time. To the best of our knowledge, this is the first general framework for obtaining memory-constrained algorithms.