On the Optimal Nested Ordered Algorithm

Viktor Skorniakov ()
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Viktor Skorniakov: Vilnius University

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 4, 1-15

Abstract: Abstract Kurtz and Sidi (IEEE Trans Commun 36(12):1316–1323, 1988) have introduced an Optimal Nested Ordered (ONO) Group Testing procedure and proposed a recursive algorithm for its determination. Having $$\varvec{n}$$ items to be classified, the order of their algorithm is $$\varvec{O}\varvec{(}\varvec{n}^{\varvec{3}}\varvec{)}$$ . We discuss an alternative dynamic tree-based approach. It was discovered by Hwang (1973) fifteen years before the appearance of Kurtz and Sidi (IEEE Trans Commun 36(12):1316–1323, 1988) and remained unrecognized. It is an aim of this paper to link these two works. Our analysis demonstrates that Hwang’s version complexity is $$\varvec{O}\varvec{(}\varvec{n}^{\varvec{2}}\varvec{\ln }\, \varvec{n}\varvec{)}$$ and in some special cases it can be reduced to $$\varvec{O}\varvec{(}\varvec{n}^{\varvec{2}}\varvec{)}$$ .

Keywords: Group testing; Optimal nested ordered algorithm; Dynamic procedure; Complexity; 68W40; 68Q87; 94D99 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10211-4

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