Algorithmica

, Volume 72, Issue 4, pp 1097–1129 | Cite as

Space–Time Trade-offs for Stack-Based Algorithms

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

Abstract

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 \(\mathcal {A}\) that runs in \(O(n)\) time using a stack of length \(\Theta (n)\), we can modify it so that it runs in \(O(n^2\log n/2^s)\) time using a workspace of \(O(s)\) variables (for any \(s\in o(\log n)\)) or \(O(n^{1+1/\log p})\) time using \(O(p\log _p n)\) variables (for any \(2\le p\le n\)). 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 \(O(\log n)\) 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.

Keywords

Memory constrained algorithms Space–time trade-off Stack algorithms Constant workspace 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Luis Barba
    • 1
  • Matias Korman
    • 2
  • Stefan Langerman
    • 3
  • Kunihiko Sadakane
    • 4
  • Rodrigo I. Silveira
    • 5
  1. 1.School of Computer Science, Carleton UniversityOttawaCanada
  2. 2.National Institute of InformaticsTokyoJapan
  3. 3.Département d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium
  4. 4.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan
  5. 5.Dept. de MatemáticaUniversidade de AveiroAveiroPortugal

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