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386
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
On the VCdimension of neural networks with binary weights
, 1996
"... Abstract: We investigate the VCdimension of the perceptron and simple twolayer networks like the committee and the paritymachine with weights restricted to values ±1. For binary inputs, the VCdimension is determined by atypical pattern sets, i.e. it cannot be found by replica analysis or numeri ..."
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or numerical Monte Carlo sampling. For small systems, exhaustive enumerations yield exact results. For systems that are too large for enumerations, number theoretic arguments give lower bounds for the VCdimension. For the Ising perceptron, the VCdimension is probably larger than N/2.
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 ..."
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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
On Beamforming with Finite Rate Feedback in Multiple Antenna Systems
, 2003
"... In this paper, we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any f ..."
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Cited by 272 (14 self)
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finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t 1)2 , where B
A Tight Lower Bound for kSet Agreement
, 1993
"... We prove tight bounds on the time needed to solve kset agreement, a natural generalization of consensus. We analyze this problem in a synchronous, messagepassing model where processors fail by crashing. We prove alower bound of bf=kc+1 rounds of communication for solutions to kset agreement that ..."
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Cited by 18 (9 self)
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We prove tight bounds on the time needed to solve kset agreement, a natural generalization of consensus. We analyze this problem in a synchronous, messagepassing model where processors fail by crashing. We prove alower bound of bf=kc+1 rounds of communication for solutions to kset agreement
Tight Lower Bounds for the Size of EpsilonNets (Extended Abstract)
 SCG '11
, 2011
"... According to a well known theorem of Haussler and Welzl (1987), any range space of bounded VCdimension admits an εnet of size O () 1 1 log. Using probabilistic techniques, ε ε Pach and Woeginger (1990) showed that there exist range spaces of VCdimension 2, for which the above bound is sharp. The ..."
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According to a well known theorem of Haussler and Welzl (1987), any range space of bounded VCdimension admits an εnet of size O () 1 1 log. Using probabilistic techniques, ε ε Pach and Woeginger (1990) showed that there exist range spaces of VCdimension 2, for which the above bound is sharp
LOWER BOUNDS FOR DIOPHANTINE APPROXIMATIONS
, 1996
"... We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. ¿From this algorithm, we derive a new procedure for the decision of consistency of polynomial equation ..."
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Cited by 70 (26 self)
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We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. ¿From this algorithm, we derive a new procedure for the decision of consistency of polynomial equation
Improved lower bound on the geometric dilation of point sets
 EWCG 2005
, 2005
"... Let G be an embedded planar graph whose edges are curves. The detour between two points p and q (on edges or vertices) of G is the length of a shortest path connecting p and q in G divided by their Euclidean distance pq. The maximum detour over all pairs of points is called the geometric dilation ..."
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Cited by 1 (1 self)
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δ(G). EbbersBaumann, Grüne and Klein have shown that every finite point set is contained in a planar graph whose geometric dilation is at most 1.678, and some point sets require graphs with dilation δ ≥ π/2 ≈ 1.57. They conjectured that the lower bound is not tight. We use new ideas, a disk packing
The VC Dimension for Mixtures of Binary Classifiers
"... The mixturesofexperts (ME) methodology provides a tool of classification when experts of logistic regression models or Bernoulli models are mixed according to a set of local weights. We show that the VapnikChervonenkis (VC) dimension of the mixturesofexperts architecture is bounded below by ..."
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The mixturesofexperts (ME) methodology provides a tool of classification when experts of logistic regression models or Bernoulli models are mixed according to a set of local weights. We show that the VapnikChervonenkis (VC) dimension of the mixturesofexperts architecture is bounded below
On the Set MultiCover Problem in Geometric Settings
 IN PROC. 25TH ANNU. ACM SYMPOS. COMPUT. GEOM
, 2009
"... We consider the set multicover problem in geometric settings. Given a set of points P and a collection of geometric shapes (or sets) F, we wish to nd a minimum cardinality subset of F such that each point p ∈ P is covered by (contained in) at least d(p) sets. Here d(p) is an integer demand (require ..."
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Cited by 19 (4 self)
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cover problem as well. In particular, we obtain an O(log opt) approximation for set systems of bounded VCdimension, and an O(1) approximation for covering points by halfspaces in three dimensions and for some other classes of shapes.
Results 1  10
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386