Statistical Physics of Group Testing

Abstract

This paper provides a short introduction to the group testing problem, and reviews various aspects of its statistical physics formulation. Two main issues are discussed: the optimal design of pools used in a two-stage testing experiment, like the one often used in medical or biological applications, and the inference problem of detecting defective items based on pool diagnosis. The paper is largely based on: M. M\'ezard and C. Toninelli, arXiv:0706.3104, and M. M\'ezard and M. Tarzia {\it Phys. Rev. E} {\bf 76}, 041124 (2007).