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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 11 (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
VCDimensions For Graphs
, 1994
"... We study set systems over the vertex set (or edge set) of some graph that are induced by special graph properties like clique, connectedness, path, star, tree, etc. We derive a variety of combinatorial and computational results on the VC (VapnikChervonenkis) dimension of these set systems. For most ..."
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Cited by 1 (0 self)
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. For most of these set systems (e.g. for the systems induced by trees, connected sets, or paths), computing the VCdimension is an NPhard problem. Moreover, determining the VCdimension for set systems induced by neighborhoods of single vertices is complete for the class LogNP. In contrast
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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problem is well understood, Bronnimann and Goodrich[3] presented improved approximation algorithms for the problem in the case that the input instances have bounded VapnikChervonenkis (VC) dimension.
Lower bounds for evolution strategies using VCdimension
 PARALLEL PROBLEM SOLVING FROM NATURE, DORTMUND: GERMANY (2008)
, 2008
"... We derive lower bounds for comparisonbased or selectionbased algorithms, improving existing results in the continuous setting, and extending them to nontrivial results in the discrete case. We introduce for that the use of the VCdimension of the level sets of the fitness functions; results are t ..."
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Cited by 12 (5 self)
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We derive lower bounds for comparisonbased or selectionbased algorithms, improving existing results in the continuous setting, and extending them to nontrivial results in the discrete case. We introduce for that the use of the VCdimension of the level sets of the fitness functions; results
Tight bounds on the maximum size of a set of permutations with bounded VCdimension
 In Proc. Symposium on Discrete Algorithms
, 2012
"... The VCdimension of a family P of npermutations is the largest integer k such that the set of restrictions of the permutations in P on some ktuple of positions is the set of all k! permutation patterns. Let rk(n) be the maximum size of a set of npermutations with VCdimension k. Raz showed that r2 ..."
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Cited by 10 (2 self)
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The VCdimension of a family P of npermutations is the largest integer k such that the set of restrictions of the permutations in P on some ktuple of positions is the set of all k! permutation patterns. Let rk(n) be the maximum size of a set of npermutations with VCdimension k. Raz showed that r
VCdimension and shortest path algorithms
"... We explore the relationship between VCdimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VCdimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms for the p ..."
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Cited by 17 (5 self)
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We explore the relationship between VCdimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VCdimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Shape modeling with front propagation: A level set approach
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... Abstract Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods ..."
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Cited by 804 (20 self)
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secting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a “HamiltonJacob? ’ type equation written for a function in which the interface is a particular level set. A speed term synthesizpd from the image is used to stop the interface
DISTRIBUTED SYSTEMS
, 1985
"... Growth of distributed systems has attained unstoppable momentum. If we better understood how to think about, analyze, and design distributed systems, we could direct their implementation with more confidence. ..."
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Cited by 755 (1 self)
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Growth of distributed systems has attained unstoppable momentum. If we better understood how to think about, analyze, and design distributed systems, we could direct their implementation with more confidence.
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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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
Results 1  10
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483,638