Note on covering monotone orthogonal polygons with star-shaped polygons

Authors:
Andrzej Lingas;Agnieszka Wasylewicz;Paweł Żyliński
Affiliations:
Department of Computer Science, Lund University, 221 00 Lund, Sweden;Department of Mathematics, Oslo University, NO-0316 Oslo, Norway;Institute of Computer Science, University of Gdańsk, 80-952 Gdańsk, Poland
Venue:
Information Processing Letters
Year:
2007

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Abstract

In 1986, Keil provided an O(n2) time algorithm for the problem of covering monotone orthogonal polygons with the minimum number of r-star-shaped orthogonal polygons. This was later improved to O(n) time and space by Gewali et al. in [L. Gewali, M. Keil, S.C. Ntafos, On covering orthogonal polygons with star-shaped polygons, Information Sciences 65 (1992) 45-63]. In this paper we simplify the latter algorithm-we show that with a little modification, the first step Sweep1 of the discussed algorithm-which computes the top ceilings of horizontal grid segments-can be omitted. In addition, for the minimum orthogonal guard problem in the considered class of polygons, our approach provides a linear time algorithm which uses O(k) additional space, where k is the size of the optimal solution-the algorithm in [L. Gewali, M. Keil, S.C. Ntafos, On covering orthogonal polygons with star-shaped polygons, Information Sciences 65 (1992) 45-63] uses both O(n) time and O(n) additional space.