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Shatter functions of (geometric) hypergraphs
[2017 Discrete Math 세미나 ]
Date: 2017-09-25
Speaker : Xavier Goaoc (Université Paris-Est, Marne-la-Vallée, France)
Abstract : In combinatorial and computational geometry, the complexity of a system of sets is often studied via its shatter function. I will introduce these functions, and discuss how their asymptotic growth rate is governed from a single of its values, in the spirit of the classical notion of “Vapnik-Chernonenkis dimension” of hypergraphs. In particular, I will describe a probabilistic construction that refutes a conjecture of Bondy and Hajnal. This is joint work with Boris Bukh (https://arxiv.org/abs/1701.06632). The talk will start from first principles.
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