New and improved BIST diagnosis methods from combinatorial Group testing theory

We consider two combinatorial problems. The first we call ``search with wildcards'': given an unknown $n$-bit string $x$, and the ability to check whether any subset of the bits of $x$ is equal to a provided query string, the goal is to output $x$. We give a nearly optimal $O(\sqrt{n} \log n)$ quantum query algorithm for search with wildcards, beating the classical lower bound of $\Omega(n)$ queries. Rather than using amplitude amplification or a quantum walk, our algorithm is ultimately based on the solution to a state discrimination problem. The second problem we consider is combinatorial group testing, which is the task of identifying a subset of at most $k$ special items out of a set of $n$ items, given the ability to make queries of the form ``does the set $S$ contain any special items?''\ for any subset $S$ of the $n$ items. We give a simple quantum algorithm which uses $O(k)$ queries to solve this problem, as compared with the classical lower bound of $\Omega(k \log(n/k))$ queries.

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A Non-Adaptive Combinatorial Group Testing Strategy to Facilitate Healthcare Worker Screening During the Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) Outbreak

10.1101/2020.07.21.20157677 ◽

2020 ◽

Author(s):

John Henry McDermott ◽

Duncan Stoddard ◽

Peter Woolf ◽

Jamie M Ellingford ◽

David Gokhale ◽

...

Keyword(s):

Web Application ◽

Group Testing ◽

Return Of Results ◽

Testing Strategy ◽

Healthcare Facilities ◽

Staff Members ◽

High Prevalence ◽

Combinatorial Group Testing ◽

Low Prevalence ◽

Combinatorial Group

Background: Regular SARS-CoV-2 testing of healthcare workers (HCWs) has been proposed to prevent healthcare facilities becoming persistent reservoirs of infectivity. Using monoplex testing, widespread screening would be prohibitively expensive, and throughput may not meet demand. We propose a non-adaptive combinatorial (NAC) group-testing strategy to increase throughput and facilitate rapid turnaround via a single round of testing. Methods: NAC matrices were constructed for sample sizes of 700, 350 and 250 with replicates of 2, 4 and 5, respectively. Matrix performance was tested by simulation under different SARS-CoV-2 prevalence scenarios of 0.1-10%, with each simulation ran for 10,000 iterations. Outcomes included the proportions of re-tests required and the proportion of true negatives identified. NAC matrices were compared to Dorfman Sequential (DS) approaches. A web application (www.samplepooling.com) was designed to decode results. Findings: NAC matrices performed well at low prevalence levels with an average number of 585 tests saved per assay in the n=700 matrix at a 1% prevalence. As prevalence increased, matrix performance deteriorated with n=250 most tolerant. In simulations of low to medium (0.1%-3%) prevalence levels all NAC matrices were superior, as measured by fewer repeated tests required, to the DS approaches. At very high prevalence levels (10%) the DS matrix was marginally superior, however both group testing approaches performed poorly at high prevalence levels. Interpretation: This testing strategy maximises the proportion of samples resolved after a single round of testing, allowing prompt return of results to staff members. Using the methodology described here, laboratories can adapt their testing scheme based on required throughput and the current population prevalence, facilitating a data-driven testing strategy.

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An Efficient Scheme for Hard Disk Integrity Check in Digital Forensics by Hashing with Combinatorial Group Testing

International Journal of Digital Content Technology and its Applications ◽

10.4156/jdcta.vol5.issue2.35 ◽

2011 ◽

Vol 5 (2) ◽

pp. 300-308 ◽

Cited By ~ 4

Author(s):

Junbin Fang ◽

Zoe L. Jiang ◽

S.M. Yiu ◽

Lucas C.K. Hui

Keyword(s):

Digital Forensics ◽

Group Testing ◽

Hard Disk ◽

Efficient Scheme ◽

Combinatorial Group Testing ◽

Combinatorial Group ◽

Integrity Check

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Strongly separable matrices for nonadaptive combinatorial group testing

Discrete Applied Mathematics ◽

10.1016/j.dam.2020.11.022 ◽

2021 ◽

Vol 291 ◽

pp. 180-187

Author(s):

Jinping Fan ◽

Hung-Lin Fu ◽

Yujie Gu ◽

Ying Miao ◽

Maiko Shigeno

Keyword(s):

Group Testing ◽

Combinatorial Group Testing ◽

Combinatorial Group

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A Combinatorial Model of Two-Sided Search

International Journal of Foundations of Computer Science ◽

10.1142/s0129054118410022 ◽

2018 ◽

Vol 29 (04) ◽

pp. 481-504 ◽

Cited By ~ 1

Author(s):

Harout Aydinian ◽

Ferdinando Cicalese ◽

Christian Deppe ◽

Vladimir Lebedev

Keyword(s):

Search Strategy ◽

Group Testing ◽

Time Instant ◽

New Model ◽

Minimum Number ◽

Combinatorial Model ◽

Accuracy Parameter ◽

Unknown Node ◽

Combinatorial Group Testing ◽

Combinatorial Group

We study a new model of combinatorial group testing: the item to be found (a.k.a. the target) occupies an unknown node in a graph. At each time instant, we can test (or query) a subset of the nodes and learn whether the target occupies any of such nodes. Immediately after the result of the test is available, the target can move to any node adjacent to its present location. The search finishes when we are able to locate the object with some predefined accuracy [Formula: see text] (a parameter fixed beforehand), i.e., to indicate a set of [Formula: see text] nodes that includes the location of the object. In this paper we study two types of problems related to the above model: (i) what is the minimum value of the accuracy parameter for which a search strategy in the above sense exists; (ii) given the accuracy, what is the minimum number of tests that allow to locate the target. We study these questions on paths, cycles, and trees as underlying graphs and provide tight answers for the above questions. We also consider a restricted variant of the problem, where the number of moves of the target is bounded.

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