Adaptive Learning a Hidden Hypergraph

نویسندگان

  • Arkadii G. D'yachkov
  • Ilya Vorobyev
  • Nikita Polyanskii
  • Vladislav Shchukin
چکیده

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph Hun = H(V, E) by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family F(t, s, `) of localized hypergraphs for which the total number of vertices |V | = t, the number of edges |E| 6 s, s ¿ t, and the cardinality of any edge |e| 6 `, ` ¿ t. Our goal is to identify all edges of Hun ∈ F(t, s, `) by using the minimal number of tests. We provide an adaptive algorithm that matches the information theory bound, i.e., the total number of tests of the algorithm in the worst case is at most s` log2 t(1 + o(1)).

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عنوان ژورنال:
  • CoRR

دوره abs/1607.00507  شماره 

صفحات  -

تاریخ انتشار 2016