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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2013.281
URN: urn:nbn:de:0030-drops-39411
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/3941/
Barba, Luis ;
Korman, Matias ;
Langerman, Stefan ;
Silveira, Rodrigo I. ;
Sadakane, Kunihiko
Space-Time Trade-offs for Stack-Based Algorithms
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},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2013/3941},
URN = {urn:nbn:de:0030-drops-39411},
doi = {10.4230/LIPIcs.STACS.2013.281},
annote = {Keywords: space-time trade-off, constant workspace, stack algorithms}
}
Keywords: |
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space-time trade-off, constant workspace, stack algorithms |
Collection: |
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30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013) |
Issue Date: |
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2013 |
Date of publication: |
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26.02.2013 |