An Asymptotic Isoperimetric Inequality |
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| Authors: | N. Alon R. Boppana J. Spencer |
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| Affiliation: | (1) Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel, e-mail: noga@math.tau.ac.il, US;(2) Dept. of Comp. Sci., Courant Institute, New York University, New York, NY 10012, USA, e-mail: boppana@cs.nyu.edu, US;(3) Dept. of Math. & Comp. Sci., Courant Institute, New York University, New York, NY 10012, USA, e-mail: spencer@cs.nyu.edu, US |
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| Abstract: | For a finite metric space V with a metric , let V n be the metric space in which the distance between (a 1 , . . ., a n ) and (b 1 , . . ., b n ) is the sum . We obtain an asymptotic formula for the logarithm of the maximum possible number of points in V n of distance at least d from a set of half the points of V n , when n tends to infinity and d satisfies . Submitted: September 1997, Final version: November 1997 |
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