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EdgeIsoperimetric Problems for Cartesian Powers of Regular Graphs
 Theor. Comput. Sci
"... We consider an edgeisoperimetric problem (EIP) on the cartesian powers of graphs. One of our objectives is to extend the list of graphs for whose cartesian powers the lexicographic order provides nested solutions for the EIP. We present several new classes of such graphs that include as special cas ..."
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Cited by 4 (0 self)
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cases all presently known graphs with this property. Our new results are applied to derive best possible edgeisoperimetric inequalities for the cartesian powers of arbitrary regular, resp. regular bipartite, graphs with a high density. 1 Introduction Let G = (V G ; EG ) be a graph and A; B VG
Edgeisoperimetric inequalities and influences
 In Combinatorics, Probability, and Computing
, 2006
"... Abstract We give a combinatorial proof of the result of Kahn, Kalai, and Linial [19], which statesthat every balanced boolean function on the ndimensional boolean cube has a variable with influence of at least \Omega i log nn j. The methods of the proof are then used to recover additional isoperime ..."
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Cited by 15 (2 self)
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isoperimetric results forthe cube, with improved constants. We also state some conjectures about optimal constants and discuss their possible implications.
An EdgeIsoperimetric Problem for Powers of the Petersen Graph
, 1998
"... In this paper we introduce a new order on the set of ndimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph P n , dened as the n th cartesian power of the wellknown Petersen graph. The cutwidth and wirelength of P n are also deri ..."
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Cited by 3 (3 self)
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In this paper we introduce a new order on the set of ndimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph P n , dened as the n th cartesian power of the wellknown Petersen graph. The cutwidth and wirelength of P n are also
General edgeisoperimetric inequalities  Part I. Informationtheoretical methods
"... In Combinatorics we often meet two kinds of extremal problems. In one kind optimal configurations consist of "objects", which are somehow uniformly spread in the space under consideration, and in the other kind optimal configurations consist of "objects", which are some how comp ..."
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Cited by 12 (0 self)
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compressed. To the first kind belong packing, covering and coding problems, whereas diametric (especially of ErdosKoRadotype), vertex and edgeisoperimetric problems belong to the second kind. For many problems of the spreading type the probabilistic method gives good or even asymptotically optimal
The Edgeisoperimetric Number of Generalized Cylinders
"... A ddimensional generalized cylinder G d is the Cartesian product of d graphs, each of which is a path graph or a cycle graph. In this paper, we use an embedding technique to show that the edgeisoperimetric number i(G d ) is given by i(G d ) = minfi(P k ); i(C l )g where P k and C l are th ..."
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Cited by 2 (2 self)
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A ddimensional generalized cylinder G d is the Cartesian product of d graphs, each of which is a path graph or a cycle graph. In this paper, we use an embedding technique to show that the edgeisoperimetric number i(G d ) is given by i(G d ) = minfi(P k ); i(C l )g where P k and C l
APPROXIMATE CONVEXITY AND AN EDGEISOPERIMETRIC ESTIMATE
"... Abstract. We study extremal properties of the function F (x): = min{k‖x‖1−1/k: k ≥ 1}, x ∈ [0, 1], where ‖x ‖ = min{x, 1 − x}. In particular, we show that F is the pointwise largest function of the class of all realvalued functions f defined on the interval [0, 1], and satisfying the relaxed conve ..."
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, then the number of edges from A to its complement G \A in the directed Cayley graph induced by S on G is
Qualitative process theory
 MIT AI Lab Memo
, 1982
"... Objects move, collide, flow, bend, heat up, cool down, stretch, compress. and boil. These and other things that cause changes in objects over time are intuitively characterized as processes. To understand commonsense physical reasoning and make programs that interact with the physical world as well ..."
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Cited by 884 (92 self)
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motivates a new qualitative representation for quantity in terms of inequalities, called the quantity space. This paper describes the basic concepts of qualitative process theory, several different kinds of reasoning that can be performed with them, and discusses its implications for causal reasoning
Active Contours without Edges
, 2001
"... In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, MumfordShah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy ..."
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Cited by 1188 (37 self)
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In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, MumfordShah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "meancurvature flow"like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We will give a numerical algorithm using finite differences. Finally, we will present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.
A computational approach to edge detection
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1986
"... AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal ..."
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Cited by 4621 (0 self)
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AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal
Results 1  10
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