Space-time trade-offs for stack-based algorithms

Luis Barba, Matias Korman, Stefan Langerman, Rodrigo I. Silveira, Kunihiko Sadakane

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

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 memoryconstrained algorithms. Given an algorithm A that runs in O(n) time using a stack of length ≤(n), we can modify it so that it runs in O(n2/2s) time using a workspace of O(s) variables (for any s 2 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.

Original languageEnglish
Title of host publication30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013
Pages281-292
Number of pages12
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013 - Kiel, Germany
Duration: 2013 Feb 272013 Mar 2

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume20
ISSN (Print)1868-8969

Other

Other30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013
CountryGermany
CityKiel
Period13/2/2713/3/2

Keywords

  • Constant workspace
  • Off
  • Space
  • Stack algorithms
  • Time trade

ASJC Scopus subject areas

  • Software

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