### Journals Information

**
Mathematics and Statistics Vol. 10(4), pp. 808 - 815 DOI: 10.13189/ms.2022.100411 Reprint (PDF) (192Kb) **

## Subset Intersection Group Testing Strategy

**Maheswaran Srinivasan ^{*}**

Institute of Management Technology, Nagpur, Maharashtra, India

**ABSTRACT**

Many a time, items can be classified as defective or non-defective and the objective is to identify all the defective items, if any, in the population. The concept of group testing deals with identifying all such defective items using a minimum number of tests. This paper proposes probabilistic group testing through a subset intersection group testing strategy. The proposed algorithm 'Subset Intersection Group Testing Strategy' deals with dividing the whole population, if it is positive, into different rows and columns and individually testing all the defective rows and columns. Through this proposed strategy, the number of group tests is either always one when no defective is found or 1+r+c, where r and c denote the number of rows and columns, when at least one defective is found. The proposed algorithms are validated using simulation for different combinations of group size and the incidence probability of an item being defective (p) and implications are drawn. The results indicate that the average number of total tests required is smaller when p is small and considerably increases as p increases. Therefore, for the smaller values of p, this proposed strategy is more effective. Also, an attempt is made to estimate an upper bound for the number of tests through this strategy in various scenarios.

**KEYWORDS**

Probabilistic Group Testing, Expected Number of Tests, Relative Efficiency, Simulation

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Maheswaran Srinivasan , "Subset Intersection Group Testing Strategy," Mathematics and Statistics, Vol. 10, No. 4, pp. 808 - 815, 2022. DOI: 10.13189/ms.2022.100411.

(b). APA Format:

Maheswaran Srinivasan (2022). Subset Intersection Group Testing Strategy. Mathematics and Statistics, 10(4), 808 - 815. DOI: 10.13189/ms.2022.100411.