Elsevier

Discrete Applied Mathematics

Volume 164, Part 1, 19 February 2014, Pages 92-99
Discrete Applied Mathematics

Covering points with orthogonal polygons

https://doi.org/10.1016/j.dam.2012.01.018Get rights and content
Under an Elsevier user license
open archive

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.

Keywords

Covering
Orthogonal polygon
NP-completeness

Cited by (0)

This article is an extended version of Evrendilek et al. (2010) [4] which was presented in ISCO’10.