TY - GEN

T1 - Space-time trade-offs for stack-based algorithms

AU - Barba, Luis

AU - Korman, Matias

AU - Langerman, Stefan

AU - Silveira, Rodrigo I.

AU - Sadakane, Kunihiko

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Constant workspace

KW - Off

KW - Space

KW - Stack algorithms

KW - Time trade

UR - http://www.scopus.com/inward/record.url?scp=84892623650&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892623650&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.STACS.2013.281

DO - 10.4230/LIPIcs.STACS.2013.281

M3 - Conference contribution

AN - SCOPUS:84892623650

SN - 9783939897507

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 281

EP - 292

BT - 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013

T2 - 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013

Y2 - 27 February 2013 through 2 March 2013

ER -