Brief Course Description

This is a short course on algorithmic combinatorial group testing and applications. The basic setting of the group testing problem is to identify a subset of "positive" items from a huge item population using as few "tests" as possible. The meaning of "positive", "tests" and "items" are dependent on the application. For example, dated back to World War II when the area of group testing started, "items" are blood samples, "positive" means syphilis-positive, and a "test" contains a pool of blood samples which results in a positive outcome if there is at least one sample in the pool positive for syphylis. This basic problem paradigm has found numerous applications in biology, cryptography, networking, signal processing, coding theory, statistical learning theory, data streaming, etc. This short course aims to introduce group testing from a computational view point, where not only the constructions of group testing strategies are of interest, but also the computational efficiency of both the construction and the decoding procedures are studied. We will also briefly introduce the probabilistic method, algorithmic coding theory, and several direct applications of group testing.

Instructor

Prerequisites

Basic knowledge of probability theory. (We assume that you have studied some introductory probability course/book before.) Basic knowledge of algorithm analysis and design. Some familiarity with linear algebra.

Work Load

  • About 30 pages of fairly dense reading per week.
  • Roughly 5 homework problems per week, most of which are routine, one of which is exploratory.

Some reference materials.

You're not required to purchase any book. In fact, except for a few very basic results, our coverage will be on materials not covered in any books yet.

  • Hung Q. Ngo, Ely Porat, and Atri Rudra, ``Efficiently Decodable Error-Correcting List Disjunct Matrices and Applications,'' in Proceedings of The 38th International Colloquium on Automata, Languages and Programming (ICALP 2011), July 04 -- 08, 2011, Zurich, Switzerland.
  • Piotr Indyk, Hung Q. Ngo, and Atri Rudra, ``Efficiently Decodable Non-adaptive Group Testing,'' in Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2010), Austin, Texas, Jan 17-19, 2010.
  • Ding-Zhu Du and Frank Hwang, Combinatorial Group Testing and Its Applications (Applied Mathematics)
  • Hung Q. Ngo, and Ding-Zhu Du, A Survey on Combinatorial Group Testing Algorithms with Applications to DNA Library Screening, in Discrete mathematical problems with medical applications (New Brunswick, NJ), 171--182, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 55, Amer. Math. Soc., Providence, RI, 2000. [ pdf ]. This survey is very old, and becoming irrelevant. A new survey will come out soon, hopefully!