Results 1  10
of
18,428
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 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
to these intractability results, we show that the VCdimension for set systems induced by stars is computable in polynomial time. For set systems induced by paths or cycles, we determine the extremal graphs G with the minimum number of edges such that VCP (G) k. Finally, we show a close relation between the VC
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 ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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.
Counting dpolytopes with d + 3 vertices
, 2008
"... We completely solve the problem of enumerating combinatorially inequivalent ddimensional polytopes with d + 3 vertices. A first solution of this problem, by Lloyd, was published in 1970. But the obtained counting formula was not correct, as pointed out in the new edition of Grünbaum’s book. We both ..."
Abstract
 Add to MetaCart
both correct the mistake of Lloyd and propose a more detailed and selfcontained solution, relying on similar preliminaries but using then a different enumeration method involving automata. In addition, we introduce and solve the problem of counting oriented and achiral (i.e. stable under reflection) dpolytopes
The VCDimension of Graphs with Respect to kConnected Subgraphs
"... We study the VCdimension of the set system on the vertex set of some graph which is induced by the family of its kconnected subgraphs. In particular, we give upper and lower bounds for the VCdimension. Moreover, we show that computing the VCdimension is NPcomplete and that it remains NPcomplet ..."
Abstract
 Add to MetaCart
We study the VCdimension of the set system on the vertex set of some graph which is induced by the family of its kconnected subgraphs. In particular, we give upper and lower bounds for the VCdimension. Moreover, we show that computing the VCdimension is NPcomplete and that it remains NP
FEW SMOOTH dPOLYTOPES WITH N LATTICE POINTS
, 2011
"... We prove that, for fixed N there exist only finitely many embeddings of Qfactorial toric varieties X into P N that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and N, there are only finitely many smooth dpolytopes wit ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We prove that, for fixed N there exist only finitely many embeddings of Qfactorial toric varieties X into P N that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and N, there are only finitely many smooth dpolytopes
An Improved Bound on the VCDimension of Neural Networks with Polynomial . . .
, 2002
"... We derive an improved upper bound for the VCdimension of neural networks with polynomial activation functions. This improved bound is based on a result of Rojas [Roj00] on the number of connected components of a semialgebraic set. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
We derive an improved upper bound for the VCdimension of neural networks with polynomial activation functions. This improved bound is based on a result of Rojas [Roj00] on the number of connected components of a semialgebraic set.
Hitting sets when the VCdimension is small
, 2004
"... We present an approximation algorithm for the hitting set problem when the VCdimension of the set system is small. Our algorithm builds on Pach & Agarwal [7], and we show how it can be parallelized and extended to the minimum cost hitting set problem. The running time of the proposed algorithm ..."
Abstract
 Add to MetaCart
We present an approximation algorithm for the hitting set problem when the VCdimension of the set system is small. Our algorithm builds on Pach & Agarwal [7], and we show how it can be parallelized and extended to the minimum cost hitting set problem. The running time of the proposed algorithm
On compact hyperbolic Coxeter dpolytopes with d+4 facets
, 2007
"... We show that there is no compact hyperbolic Coxeter dpolytope with d+4 facets for d≥8. This bound is sharp: examples of such polytopes up to dimension 7 were found by Bugaenko [Bu1]. We also show that in dimension ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We show that there is no compact hyperbolic Coxeter dpolytope with d+4 facets for d≥8. This bound is sharp: examples of such polytopes up to dimension 7 were found by Bugaenko [Bu1]. We also show that in dimension
Results 1  10
of
18,428