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### Space-Time Trade-offs for Stack-Based Algorithms

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### Abstract

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 A that runs in O(n) time using a stack of length Theta(n), we can modify it so that it runs in O(n^2/2^s) time using a workspace of O(s) variables (for any s \in o(log n)) or O(n log n/log p)\$ time using O(p log n/log p) 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 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.

### BibTeX - Entry

@InProceedings{barba_et_al:LIPIcs:2013:3941,
author =	{Luis Barba and Matias Korman and Stefan  Langerman and Rodrigo I. Silveira and Kunihiko Sadakane},
title =	{{Space-Time Trade-offs for Stack-Based Algorithms}},
booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages =	{281--292},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-50-7},
ISSN =	{1868-8969},
year =	{2013},
volume =	{20},
editor =	{Natacha Portier and Thomas Wilke},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},