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Guarding Polyhedral Terrains
, 1992
"... We prove that b c vertex guards are always sufficient and sometimes necessary to guard the surface of an nvertex polyhedral terrain. We also show that b guards are sometimes necessary to guard the surface of an nvertex polyhedral terrain. ..."
Abstract

Cited by 26 (6 self)
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We prove that b c vertex guards are always sufficient and sometimes necessary to guard the surface of an nvertex polyhedral terrain. We also show that b guards are sometimes necessary to guard the surface of an nvertex polyhedral terrain.
Efficient Algorithms for Guarding or Illuminating the Surface of a Polyhedral Terrain
 Proceedings of the 8th Canadian Conference on Computational Geometry, volume 5 of International Informatics Series
, 1996
"... We present efficient polynomial time algorithms that place bn=2c vertex guards which cover the surface of an nvertex polyhedral terrain, and similarly, bn=3c edge guards which cover the surface of an nvertex polyhedral terrain. The time complexity of both algorithms, dominated by the cost of fi ..."
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Cited by 6 (0 self)
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We present efficient polynomial time algorithms that place bn=2c vertex guards which cover the surface of an nvertex polyhedral terrain, and similarly, bn=3c edge guards which cover the surface of an nvertex polyhedral terrain. The time complexity of both algorithms, dominated by the cost of finding a maximum matching in a graph, is O(n ).
WorstCaseOptimal Algorithms for Guarding Planar Graphs and Polyhedral Surfaces
, 2003
"... We present an optimal \Theta (n)time algorithm for the selection of a subset of the vertices of an nvertex plane graph G so that each of the faces of G is covered by (i.e. incident with) one or more of the selected vertices. At most bn=2c vertices are selected, matching the worstcase requiremen ..."
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Cited by 4 (0 self)
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We present an optimal \Theta (n)time algorithm for the selection of a subset of the vertices of an nvertex plane graph G so that each of the faces of G is covered by (i.e. incident with) one or more of the selected vertices. At most bn=2c vertices are selected, matching the worstcase requirement. Analogous results for edgecovers are developed for two different notions of "coverage". In particular,our lineartime algorithm selects at most n \Gamma 2 edges to strongly cover G, at most bn=3c diagonals to cover G, and in the case where G has no quadrilateral faces, at most bn=3c edges to cover G. All these bounds are optimal in the worstcase. Most of our results flow from the study of a relaxation of thefamiliar notion of a 2coloring of a plane graph which we call a facerespecting 2coloring that permits