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VCDimension of Exterior Visibility of Polyhedra
, 2001
"... In this paper, we address the problem of finding the minimal number of viewpoints outside a polyhedron in two or three dimensions such that every point on the exterior of the polyhedron is visible from at least one of the chosen viewpoints. This problem which we call the minimum fortress guard probl ..."
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Cited by 3 (2 self)
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In this paper, we address the problem of finding the minimal number of viewpoints outside a polyhedron in two or three dimensions such that every point on the exterior of the polyhedron is visible from at least one of the chosen viewpoints. This problem which we call the minimum fortress guard
On the VCDimension of Visibility in Monotone Polygons
"... We show that the VCdimension of visibility on the boundary of a monotone polygon is exactly 6. Our lower bound construction matches the best known lower bound for simple polygons. 1 ..."
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We show that the VCdimension of visibility on the boundary of a monotone polygon is exactly 6. Our lower bound construction matches the best known lower bound for simple polygons. 1
VCdimension of Exterior Visibility
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2004
"... In this paper, we study the VapnikChervonenkis (VC)dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VCdimension of planar visibility systems is bounded by 23 if t ..."
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Cited by 13 (1 self)
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In this paper, we study the VapnikChervonenkis (VC)dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VCdimension of planar visibility systems is bounded by 23
VCdimension of visibility on terrains
 In Proc. 20th Canadian Conference on Comput. Geom
, 2008
"... A guarding problem can naturally be modeled as a set system (U, S) in which the universe U of elements is the set of points we need to guard and our collection S of sets contains, for each potential guard g, the set of points from U seen by g. We prove bounds on the maximum VCdimension of set syste ..."
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Cited by 2 (0 self)
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systems associated with guarding both 1.5D terrains (monotone chains) and 2.5D terrains (polygonal terrains). We prove that for monotone chains, the maximum VCdimension is 4 and that for polygonal terrains, the maximum VCdimension is unbounded. 1
VCDimension of Exterior Visibility Volkan Isler, Student Member, IEEE, Sampath
"... Abstract—In this paper, we study the VapnikChervonenkis (VC)dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VCdimension of planar visibility systems is bounded ..."
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Abstract—In this paper, we study the VapnikChervonenkis (VC)dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VCdimension of planar visibility systems is bounded
COLORING DENSE GRAPHS VIA VCDIMENSION
, 2010
"... Abstract. The VapnikČervonenkis dimension is a complexity measure of setsystems, or hypergraphs. Its application to graphs is usually done by considering the sets of neighborhoods of the vertices (see [1] and [5]), hence providing a setsystem. But the graph structure is lost in the process. The a ..."
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Cited by 1 (0 self)
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at least cn and arbitrarily high chromatic number, where H is a fixed graph and c a positive constant. We show how the usual VCdimension gives a short proof of the fact that trianglefree graphs with minimum degree at least n/3 have bounded chromatic number, where n is the number of vertices. Using paired
VisibilityBased PursuitEvasion in a Polygonal Environment
 International Journal of Computational Geometry and Applications
, 1997
"... This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita ..."
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Cited by 109 (25 self)
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strategy for a single pursuer. For simplyconnected free spaces, it is shown that the minimum number of pursuers required is \Theta(lg n). For multiplyconnected free spaces, the bound is \Theta( p h + lg n) pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single
Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers
 SIAM JOURNAL ON COMPUTING
"... The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant ..."
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Cited by 156 (3 self)
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The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time
On Local Transformation of Polygons with Visibility Properties
 Theoretical Computer Science
, 2002
"... One strategy for the enumeration of a class of objects is local transformation, in which new objects of the class are produced by means of a small modification of a previouslyvisited object in the same class. When local transformation is possible, the operation can be used to generate objects of th ..."
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Cited by 15 (3 self)
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of the class via random walks, and as the basis for such optimization heuristics as simulated annealing. For general simple polygons on fixed point sets, it is still not known whether the class of polygons on the set is connected via a constantsize local transformation. In this paper, we exhibit a simple
Minimum Polygon Transversals of Line Segments
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY APPLICATIONS
"... Let $ be used to denote a finite set of planar geometric objects. Define a polygon transversal of $ as a closed simple polygon that simultaneously intersects every object in $, and a minimum polygon transversal of $ as a polygon transversal of $ with minimum perimeter. If $ is a set of points the ..."
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Cited by 10 (0 self)
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then the minimum polygon transversal of $ is the convex hull of $. However, when the objects in $ have some dimension then the minimum polygon transversal and the convex hull may no longer coincide. We consider the case where $ is a set of line segments. If the line segments are constrained to lie in a fixed
Results 1  10
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