Papers › Space-Time Trade-offs for Stack-Based Algorithms
Space-Time Trade-offs for Stack-Based Algorithms
Luis Barba, Matias Korman, Stefan Langerman, Kunikiko Sadakane, Rodrigo Silveira
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In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space bottleneck is a stack into memory-constrained algorithms. Given an algorithm \alg\ that runs in O(n) time using Θ(n) variables, we can modify it so that it runs in O(n²/s) time using a workspace of O(s) variables (for any s∈o(logn)) or O(nlogn/logp) time using O(plogn/logp) 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, 1-dimensional pyramid approximation of a 1-dimensional vector, and the visibility profile of a point inside a simple polygon. Our approach exceeds or matches the best-known results for these problems in constant-workspace models (when they exist), and gives the first 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.
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