6,278 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
Engineering Art Galleries
The Art Gallery Problem is one of the most well-known problems in
Computational Geometry, with a rich history in the study of algorithms,
complexity, and variants. Recently there has been a surge in experimental work
on the problem. In this survey, we describe this work, show the chronology of
developments, and compare current algorithms, including two unpublished
versions, in an exhaustive experiment. Furthermore, we show what core
algorithmic ingredients have led to recent successes
Exploring, Engaging, Understanding in Museums
Patterns of accessibility through the space of the exhibition, connections or separations among spaces or exhibition elements, sequencing and grouping of elements, form our perceptions and shape our understanding.
Through a review of several previous studies and the presentation of new work, this paper suggests that these patterns of movement form the basis of visitor
understanding and that these effects can be deliberately controlled and elaborated through a closer examination of the influence of the visual and perceptual properties of an exhibition. Furthermore, it is argued that there is
also a spatial discourse based on patterns of access and visibility that flows in its own right, although not entirely separate from the curatorial narrative
Optimal fault-tolerant placement of relay nodes in a mission critical wireless network
The operations of many critical infrastructures (e.g., airports) heavily depend on proper functioning of the radio communication network supporting operations. As a result, such a communication network is indeed a mission-critical communication network that needs adequate protection from external electromagnetic interferences. This is usually done through radiogoniometers. Basically, by using at least three suitably deployed radiogoniometers and a gateway gathering information from them, sources of electromagnetic emissions that are not supposed to be present in the monitored area can be localised. Typically, relay nodes are used to connect radiogoniometers to the gateway. As a result, some degree of fault-tolerance for the network of relay nodes is essential in order to offer a reliable monitoring. On the other hand, deployment of relay nodes is typically quite expensive. As a result, we have two conflicting requirements: minimise costs while guaranteeing a given fault-tolerance. In this paper address the problem of computing a deployment for relay nodes that minimises the relay node network cost while at the same time guaranteeing proper working of the network even when some of the relay nodes (up to a given maximum number) become faulty (fault-tolerance). We show that the above problem can be formulated as a Mixed Integer Linear Programming (MILP) as well as a Pseudo-Boolean Satisfiability (PB-SAT) optimisation problem and present experimental results com- paring the two approaches on realistic scenarios
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