Quadratic-Time Linear-Space Algorithms for Generating Orthogonal Polygons with a Given Number of Vertices

Tomás, Ana Paula; Bajuelos, Antonio L.

doi:10.1007/978-3-540-24767-8_13

Cited by 10 publications

(11 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The worst case time complexity of the Chained Lin-Kernighan algorithm is apparently not available in the literature (Helsgaun 2009) of robots in the target area, different visual ranges for the robots, and varying degrees of clutter in the environment. A random map generator was also developed as a part of the simulator which extends a library (Tomás and Bajuelos 2004) to build rectilinear or non-rectilinear polygons with free form polygonal obstacles within the space. Maps can have different numbers of nodes and percentages of clutter.…”

Section: Evaluation and Experimental Simulationsmentioning

confidence: 99%

Multi-robot repeated area coverage

2013

View full text Add to dashboard Cite

We address the problem of repeated coverage of a target area, of any polygonal shape, by a team of robots having a limited visual range. Three distributed Clusterbased algorithms, and a method called Cyclic Coverage are introduced for the problem. The goal is to evaluate the performance of the repeated coverage algorithms under the effects of the variables: Environment Representation, and the Robots' Visual Range. A comprehensive set of performance metrics are considered, including the distance the robots travel, the frequency of visiting points in the target area, and the degree of balance in workload distribution among the robots. The Cyclic Coverage approach, used as a benchmark to compare the algorithms, produces optimal or near-optimal solutions for the single robot case under some criteria. The results can be used as a framework for choosing an appropriate combination of repeated coverage algorithm, environment representation, and the robots' visual range based on the particular scenario and the metric to be optimized.

show abstract

Section: Evaluation and Experimental Simulationsmentioning

confidence: 99%

Multi-robot repeated area coverage

2013

View full text Add to dashboard Cite

show abstract

“…The simulator can support different numbers of robots in the target area, different visual ranges for the robots, and varying degrees of clutter in the environment. A random map generator was also developed as a part of the simulator which extends a library [19] to build rectilinear or non-rectilinear polygons with free form polygonal obstacles within the space. Maps can have different numbers of nodes and percentages of clutter.…”

Section: Evaluation and Experimentsmentioning

confidence: 99%

Multi-Robot Repeated Area Coverage: Performance Optimization Under Various Visual Ranges

Fazli

Davoodi

Mackworth

2012

2012 Ninth Conference on Computer and Robot Vision

View full text Add to dashboard Cite

Abstract-We address the problem of repeated coverage of a target area, of any polygonal shape, by a team of robots having a limited visual range. Three distributed Cluster-based algorithms, and a method called Cyclic Coverage are introduced for the problem. The goal is to evaluate the performance of the repeated coverage algorithms under the effect of changes in the robots' visual range. A comprehensive set of performance metrics are considered, including the distance the robots travel, the frequency of visiting points in the target area, and the degree of balance in workload distribution among the robots. The Cyclic Coverage approach, used as a benchmark to compare the algorithms, produces optimal or near-optimal solutions for the single robot case under some criteria. The results show that the identity of the optimal repeated coverage algorithm depends on the metric and the robots' visual range.

show abstract

“…Our proof is strongly based on the Inflate-Paste method for generating grid ogons, that will be presented also at this workshop [3]. ✷…”

mentioning

confidence: 93%

“…Generic n-ogons may be obtained from a particular kind of n-ogons -the so-called grid orthogonal polygons [3], as illustrated in Fig. 1 (The reader may skip Definition 2 and Lemmas 3 and 4 if he/she has already read [3].)…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Partitioning Orthogonal Polygons by Extension of All Edges Incident to Reflex Vertices: Lower and Upper Bounds on the Number of Pieces

Bajuelos

Tomás

Marques

2004

Computational Science and Its Applications – ICCSA 2004

Self Cite

View full text Add to dashboard Cite

Given an orthogonal polygon P , let |Π(P )| be the number of rectangles that result when we partition P by extending the edges incident to reflex vertices towards INT(P ). In [4] we showed that |Π(P )| ≤ 1 + r + r 2 , where r is the number of reflex vertices of P . We shall now give sharper bounds both for maxP |Π(P )| and minP |Π(P )|. Moreover, we characterize the structure of orthogonal polygons in general position for which these new bounds are exact.

show abstract

Quadratic-Time Linear-Space Algorithms for Generating Orthogonal Polygons with a Given Number of Vertices

Cited by 10 publications

References 14 publications

Multi-robot repeated area coverage

Multi-robot repeated area coverage

Multi-Robot Repeated Area Coverage: Performance Optimization Under Various Visual Ranges

Partitioning Orthogonal Polygons by Extension of All Edges Incident to Reflex Vertices: Lower and Upper Bounds on the Number of Pieces

Contact Info

Product

Resources

About