IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Special Section on Foundations of Computer Science - Developments of the Theory of Algorithms and Computation -
Visibility Problems for Manhattan Towers
Chuzo IWAMOTOYusuke KITAGAKI
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2016 Volume E99.D Issue 3 Pages 607-614

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Abstract

A Manhattan tower is a monotone orthogonal polyhedron lying in the halfspace z ≥ 0 such that (i) its intersection with the xy-plane is a simply connected orthogonal polygon, and (ii) the horizontal cross section at higher levels is nested in that for lower levels. Here, a monotone polyhedron meets each vertical line in a single segment or not at all. We study the computational complexity of finding the minimum number of guards which can observe the side and upper surfaces of a Manhattan tower. It is shown that the vertex-guarding, edge-guarding, and face-guarding problems for Manhattan towers are NP-hard.

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© 2016 The Institute of Electronics, Information and Communication Engineers
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