International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 286-297 | Cite as

Minimum r-Star Cover of Class-3 Orthogonal Polygons

  • Leonidas PaliosEmail author
  • Petros Tzimas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)


We are interested in the problem of covering simple orthogonal polygons with the minimum number of r-stars; an orthogonal polygon is an r-star if it is star-shaped. The problem has been considered by Worman and Keil [13] who described an algorithm running in \(O(n^{17} \hbox {poly-log}\, n)\) time where n is the size of the input polygon.

In this paper, we consider the above problem on simple class-3 orthogonal polygons, i.e., orthogonal polygons that have dents along at most 3 different orientations. By taking advantage of geometric properties of these polygons, we give an output-sensitive \(O(n + k \log k)\)-time algorithm where k is the size of a minimum r-star cover; this is the first purely geometric algorithm for this problem. Ideas in this algorithm may be generalized to yield faster algorithms for the problem on general simple orthogonal polygons.


Orthogonal polygon Cover Decomposition r-star Visibility Output-sensitive 



This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALIS UOA (MIS 375891) - Investing in knowledge society through the European Social Fund.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity of IoanninaIoanninaGreece

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