Space-Time Trade-offs for Stack-Based Algorithms

TL;DR

This paper introduces the compressed stack technique, enabling the transformation of stack-based algorithms into memory-constrained versions with adjustable space-time trade-offs, applicable to various geometric problems.

Contribution

The paper presents a novel general framework for memory-constrained algorithms that achieves flexible space-time trade-offs for stack-based and geometric algorithms.

Findings

Matches or exceeds best-known results in constant-workspace models

Provides the first general framework for memory-constrained algorithms

Establishes a new trade-off between workspace size and running time

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 \alg\ that runs in O(n) time using $\Theta(n)$ variables, we can modify it so that it runs in $O(n^2/s)$ 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 $2\leq p\leq n$). 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 the first 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.