par Barba Flores, Luis 
;Korman, Matias ;Langerman, Stefan ;Sadakane, Kunihiko;Silveira, Rodrigo R.I.
Référence Algorithmica, 72, 4, page (1097-1129)
Publication Publié, 2015-08
;Korman, Matias ;Langerman, Stefan ;Sadakane, Kunihiko;Silveira, Rodrigo R.I.Référence Algorithmica, 72, 4, page (1097-1129)
Publication Publié, 2015-08
Article révisé par les pairs
| Résumé : | 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 $$\mathcal {A}$$A that runs in $$O(n)$$O(n) time using a stack of length Θ(n), we can modify it so that it runs in O(n2logn/2s) time using a workspace of $$O(s)$$O(s) variables (for any s∈o(logn)) or O(n1+1/logp) time using O(plogpn) 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, 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(logn) 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. |
