Colloquium on May 5 (Friday) 2:30 pm in Fretwell 315

 

Title: Group Testing: Some Results and Open Challenges

Abstract: Group testing has its origins in the identification of syphilis in the U.S. Army during World War II. The aim of the method is to test groups of people instead of single individuals in such a way that infected individuals are detected while the testing costs are reduced. In the last few years of the COVID-19 pandemic, the mostly-forgotten practice of group testing has been raised again in many countries as an efficient method for addressing the epidemic while facing restrictions of time and resources.

 

Consider a finite population of N items, where item i has a probability p to be defective, independent of the other units (in the generalized group testing allows different p_i). A group test is a binary test on an arbitrary group of items with two possible outcomes: all items are good, or at least one item is defective. The goal is to identify all items through group testing with the minimum expected number of tests. The optimum procedure, with respect to the expected total number of tests, is unknown even in the case where all pi are equal. In this talk, I shall review established results in the group testing literature and present new results characterizing the optimality of group testing procedures. In addition, I will discuss some open problems and conjectures. If time allows, then I will also discuss related problems of imperfect testing and the estimation of p based on grouped data.