Covering points with orthogonally convex polygons

Authors:
Burkay Genç;Cem Evrendilek;Brahim Hnich
Affiliations:
Faculty of Engineering and Computer Sciences, Izmir University of Economics, Sakarya Cad. No. 156, Balcova, Izmir, Turkey;Faculty of Engineering and Computer Sciences, Izmir University of Economics, Sakarya Cad. No. 156, Balcova, Izmir, Turkey;Faculty of Engineering and Computer Sciences, Izmir University of Economics, Sakarya Cad. No. 156, Balcova, Izmir, Turkey
Venue:
Computational Geometry: Theory and Applications
Year:
2011

Citing 2
Cited 1

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Proceedings of the 8th Canadian Conference on Computational Geometry
Reconstructing Polygons from Scanner Data

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation

Covering points with orthogonal polygons

Discrete Applied Mathematics

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Abstract

In this paper, we address the problem of covering points with orthogonally convex polygons. In particular, given a point set of size n on the plane, we aim at finding if there exists an orthogonally convex polygon such that each edge of the polygon covers exactly one point and each point is covered by exactly one edge. We show that if such a polygon exists, it may not be unique. We propose an O(nlogn) algorithm to construct such a polygon if it exists, or else report the non-existence in the same time bound. We also extend our algorithm to count all such polygons without hindering the overall time complexity. Finally, we show how to construct all k such polygons in O(nlogn+kn) time. All the proposed algorithms are fast and practical.