Covering points with orthogonal polygons

Authors:
Cem Evrendilek;Burkay Genç;Brahim Hnich
Affiliations:
Izmir University of Economics, Computer Engineering Department, Turkey;TED University, Computer Engineering Department, Turkey;Izmir University of Economics, Computer Engineering Department, Turkey
Venue:
Discrete Applied Mathematics
Year:
2014

Citing 4
Cited 0

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Abstract

We address the problem of covering points with orthogonal polygons. Specifically, given a set of n points in the plane, we investigate the existence of an orthogonal polygon such that there is a one-to-one correspondence between the points and the edges of the polygon. In an earlier paper, we have shown that constructing such a covering with an orthogonally convex polygon, if any, can be done in O(nlogn) time. In case an orthogonally convex polygon cannot cover the point set, we show in this paper that the problem of deciding whether such a point set can be covered with any orthogonal polygon is NP-complete. The problem remains NP-complete even if the orientations of the edges covering each point are specified in advance as part of the input.