On the Optimal Pairwise Group Testing Algorithm
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911012459905024 |
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| author | Skorniakov, Viktor Čižikovienė, Ugnė |
| author_facet | Skorniakov, Viktor Čižikovienė, Ugnė |
| contents | Originally suggested for the blood testing problem by Dorfman in 1943, an idea of Group Testing (GT) has found many applications in other fields as well. Among many (binomial) GT procedures introduced since then, in 1990, Yao and Hwang proposed the Pairwise Testing Algorithm (PTA) and demonstrated that PTA is the \emph{unique} optimal nested GT procedure provided the probability of contamination lies in $\left[1-\frac{\sqrt{2}}{2},\frac{3-\sqrt{5}}{2}\right]$.
Despite the fundamental nature of the result, PTA did not receive considerable attention in the literature. In particular, even its basic probabilistic properties remained unexplored. In this paper, we fill the gap by providing an exhaustive characterization of probabilistic PTA properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10331 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Optimal Pairwise Group Testing Algorithm Skorniakov, Viktor Čižikovienė, Ugnė Statistics Theory Probability 60xx (Primary), 60Fxx (Secondary) Originally suggested for the blood testing problem by Dorfman in 1943, an idea of Group Testing (GT) has found many applications in other fields as well. Among many (binomial) GT procedures introduced since then, in 1990, Yao and Hwang proposed the Pairwise Testing Algorithm (PTA) and demonstrated that PTA is the \emph{unique} optimal nested GT procedure provided the probability of contamination lies in $\left[1-\frac{\sqrt{2}}{2},\frac{3-\sqrt{5}}{2}\right]$. Despite the fundamental nature of the result, PTA did not receive considerable attention in the literature. In particular, even its basic probabilistic properties remained unexplored. In this paper, we fill the gap by providing an exhaustive characterization of probabilistic PTA properties. |
| title | On the Optimal Pairwise Group Testing Algorithm |
| topic | Statistics Theory Probability 60xx (Primary), 60Fxx (Secondary) |
| url | https://arxiv.org/abs/2207.10331 |