Adaptive Learning a Hidden Hypergraph

2016/07/02 by D'yachkov, A. G., Vorobyev, I. V., Polyanskii, N. A. +1
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1607.00507

Abstract

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph H_un=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,ℓ) of localized hypergraphs for which the total number of vertices |V| = t, the number of edges |E|≤ s, s≪ t, and the cardinality of any edge |e|≤ℓ, ℓ≪ t. Our goal is to identify all edges of H_un∈ F(t,s,ℓ) 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 sℓlog₂ t(1+o(1)).

Related

• Non-adaptive Learning of Random Hypergraphs with Queries
• Non-Adaptive Learning a Hidden Hipergraph
• Learning Low Degree Hypergraphs
• Improved bounds for group testing in arbitrary hypergraphs
• Group Testing in Arbitrary Hypergraphs and Related Combinatorial Structures