3 research outputs found
Computing a visibility polygon using few variables
We present several algorithms for computing the visibility polygon of a
simple polygon from a viewpoint inside the polygon, when the polygon
resides in read-only memory and only few working variables can be used. The
first algorithm uses a constant number of variables, and outputs the vertices
of the visibility polygon in O(n\Rout) time, where \Rout denotes the number
of reflex vertices of that are part of the output. The next two algorithms
use O(\log \Rin) variables, and output the visibility polygon in O(n\log
\Rin) randomized expected time or O(n\log^2 \Rin) deterministic time, where
\Rin is the number of reflex vertices of .Comment: 11 pages. Full version of paper in Proceedings of ISAAC 201
Space-Time Trade-offs for Stack-Based Algorithms
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 variables, we can
modify it so that it runs in time using a workspace of O(s)
variables (for any ) or time using variables (for any ). 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