Non-adaptive Group Testing on Graphs
This work addresses a generalization of hidden graph learning, with potential applications in chemical reactions and molecular biology, but appears incremental as it builds on prior studies.
The paper tackles the problem of finding a hidden defective subgraph within a larger graph using non-adaptive group testing, presenting an upper bound for the number of tests required based on the Lovász Local Lemma.
Grebinski and Kucherov (1998) and Alon et al. (2004-2005) study the problem of learning a hidden graph for some especial cases, such as hamiltonian cycle, cliques, stars, and matchings. This problem is motivated by problems in chemical reactions, molecular biology and genome sequencing. In this paper, we present a generalization of this problem. Precisely, we consider a graph G and a subgraph H of G and we assume that G contains exactly one defective subgraph isomorphic to H. The goal is to find the defective subgraph by testing whether an induced subgraph contains an edge of the defective subgraph, with the minimum number of tests. We present an upper bound for the number of tests to find the defective subgraph by using the symmetric and high probability variation of Lovász Local Lemma.