Escaping offline searchers and isoperimetric theorems
نویسندگان
چکیده
منابع مشابه
Escaping Off-Line Searchers and a Discrete Isoperimetric Theorem
We study the following pursuit-evasion game: Imagine a hunting trip on a foggy day. The field is an n x n square grid where the prey, a rabbit, is restricted to this field. The hunters and the rabbit move alternately, and each group can choose whether to stay at its current position or to move to an adjacent grid. Each hunter can see only his own grid, meaning that hunter A can not know hunter ...
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We consider subsets of the n-dimensional grid with the Manhattan metrics, (i.e. the Cartesian product of chains of lengths k1, . . . , kn) and study those of them which have maximal number of induced edges of the grid, and those which are separable from their complement by the least number of edges. The first problem was considered for k1 = · · · = kn by Bollobás and Leader [2]. Here we extend ...
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Denote by Ω = {1, . . . , n} an n–element set. For all A,B ∈ Ωk ) , the k–element subsets of Ω, define the relation ∼ as follows: A ∼ B iff A and B have a common shadow, i.e. there is a C ∈ ( Ω k−1 ) with C ⊂ A and C ⊂ B. For fixed integer α, our goal is to find a family A of k–subsets with size α, having as many as possible ∼ –relations for all pairs of its elements. For k = 2 this was achieve...
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We prove that the isoperimetric profile of a convex domain Ω with compact closure in a Riemannian manifold (M, g) satisfies a second order differential inequality which only depends on the dimension of the manifold and on a lower bound on the Ricci curvature of Ω. Regularity properties of the profile and topological consequences on isoperimetric regions arise naturally from this differential po...
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People searching for information occasionally experience difficulties finding what they want on the Web. This might happen if they cannot quite come up with the right search terms. What do searchers do when this happens? Intuitively one imagines that they will try a number of associated search terms to zero in on their intended search target. Certainly the provision of spelling suggestions and ...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2009
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2008.08.001