Identifying defective items in larger sets is a main problem with manyapplications in real life situations . We investigate old and new identifiability conditions contributing this problem both from atheoretical and applied perspective . What is the precise tradeoff between number of nodes and number of paths such that at most $k$ nodes can beidentified unambiguously ? The answer is known only for $k=1$ and we answer the question for any $k$, setting a problem implicitly left open in previous works . We use these new conditions on one side to design algorithmic heuristics to count defectivenodes in a fine-grained way, on the other side to prove the first complexityhardness results on the problem of identifying defective nodes in networks viaBNT . We introduce a random model where we study lower bounds on the number of . the number on the . number of ‘undundelicated defective nodes’ and we use this model to estimatethat number on real networks by a maximum likelihood estimate approach to estimate number on . real networks’. (4) We use a model to

Author(s) : Nicola Galesi, Fariba Ranjbar

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Keywords : number - nodes - defective - problem - real -

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