Improved algorithms for non-adaptive group testing with consecutive positives

TL;DR

This paper introduces improved non-adaptive group testing algorithms for identifying consecutive positives efficiently, reducing tests and decoding time by leveraging binary codes and specialized designs, especially when the maximum number of positives is known.

Contribution

The paper proposes novel measurement matrix constructions using binary codes and efficient designs for consecutive positives, significantly enhancing decoding speed and reducing tests in non-adaptive group testing.

Findings

Up to 300 tests identify 100 positives in 4.3 billion items.

Proposed designs halve the number of tests and decoding time when positives are consecutive.

Simulation results confirm the efficiency and superiority of the new methods.

Abstract

The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one positive and negative otherwise. In non-adaptive group testing, all tests are fixed in advance and can be performed in parallel. In this work, we consider non-adaptive group testing with consecutive positives in which the items are linearly ordered and the positives are consecutive in that order. We present two contributions here. The first is the direct use of a binary code to construct measurement matrices compared to the use of Gray code in the state-of-the-art work, which is a rearrangement of the binary code, when the maximum number of consecutive positives is known. This leads to a reduction in decoding time in practice. The second one is efficient designs to identify positives when the number of consecutive positives is known. To the best of our knowledge, this setting has not been surveyed yet. Our simulations verify the efficiency of our proposed designs. In particular, it only requires up to $300$ tests to identify up to $100$ positives in a set of $2^{32} \approx 4.3\mathrm{B}$ items in less than $300$ nanoseconds. When the maximum number of consecutive positives is known, the simulations validate the superiority of our proposed design in decoding compared to the state-of-the-art work. Moreover, when the number of consecutive positives is known, the number of tests and the decoding time are almost reduced half.