Improved Bounds for Noisy Group Testing With Constant Tests per Item

The group testing problem is concerned with identifying a small set of infected individuals in large population. At our disposal procedure that allows us to test several together. In an idealized setting, positive if and only at least one individual included negative otherwise. Significant progress was made recent years towards understanding the information-theoretic algorithmic properties this noiseless setting. paper, we consider noisy variant where results are flipped certain probability, including realistic scenario sensitivity specificity can take arbitrary values. Using design each assigned fixed number tests, derive explicit bounds for two commonly considered inference algorithms thereby naturally extend Scarlett & Cevher (2016) Johnson (2020). We provide improved performance guarantees efficient these models – indeed, parameter choices provided paper strongest currently proved.