Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

Wang, Chao; Zhao, Qing; Chuah, Chen‐Nee

doi:10.1109/tsp.2017.2780053

Cited by 18 publications

(14 citation statements)

References 54 publications

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“…The QGT problem has been extensively studied for a wide range of applications, e.g., multi-access communication, spectrum sensing, and network tomography, see, e.g., [3]- [5], and references therein. This problem was first introduced by Shapiro in [6].…”

Section: A Related Work and Applicationsmentioning

confidence: 99%

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Sparse Graph Codes for Non-adaptive Quantitative Group Testing

Karimi

Kazemi

Heidarzadeh

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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This paper considers the problem of Quantitative Group Testing (QGT). Consider a set of N items among which K items are defective. The QGT problem is to identify (all or a sufficiently large fraction of) the defective items, where the result of a test reveals the number of defective items in the tested group. In this work, we propose a nonadaptive QGT algorithm using sparse graph codes over biregular bipartite graphs with left-degree ℓ and right degree r and binary t-error-correcting BCH codes. The proposed scheme provides exact recovery with probabilistic guarantee, i.e. recovers all the defective items with high probability. In particular, we show that for the sub-linear regime where K N vanishes as K, N → ∞, the proposed algorithm requires at most m = c(t)K t log 2 ℓN c(t)K + 1 + 1 + 1 tests to recover all the defective items with probability approaching one as K, N → ∞, where c(t) depends only on t. The results of our theoretical analysis reveal that the minimum number of required tests is achieved by t = 2. The encoding and decoding of the proposed algorithm for any t ≤ 4 have the computational complexity of O(K log 2 N K ) and O(K log N K ), respectively. Our simulation results also show that the proposed algorithm significantly outperforms a non-adaptive semi-quantitative group testing algorithm recently proposed by Abdalla et al. in terms of the required number of tests for identifying all the defective items with high probability.

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Section: A Related Work and Applicationsmentioning

confidence: 99%

“…This problem was first introduced by Shapiro in [6]. Several non-adaptive and adaptive QGT strategies have been previously proposed, see, e.g., [3], [7], [8]. It was shown in [9] that any non-adaptive algorithm must perform at least (2K log 2 (N/K))/log 2 K tests.…”

Section: A Related Work and Applicationsmentioning

confidence: 99%

Sparse Graph Codes for Non-adaptive Quantitative Group Testing

Karimi

Kazemi

Heidarzadeh

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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“…The worst-case setting of the CW problem has also been extensively studied for a wide range of applications, e.g., multi-access communication, spectrum sensing, traffic monitoring, anomaly detection, and network tomography, to name a few (see, e.g., [4], and references therein). Moreover, most of these applications are being run repeatedly over time, and for such applications, the average-case performance is expected to be more relevant than the worst-case performance.…”

Section: A Related Work and Applicationsmentioning

confidence: 99%

“…Notwithstanding, the question whether these lower bounds are achievable remains open. For the worst-case setting, 2 log 2 n − 1 weighings are known to be sufficient, and this bound is achievable by a simple nested strategy (see [4,Lemma 1]). This quantity also serves as an upper bound for the average-case setting, and no tighter achievable upper bound was previously reported.…”

Section: Introductionmentioning

confidence: 99%

A Simple and Efficient Strategy for the Coin Weighing Problem with a Spring Scale

Karimi

Kazemi

Heidarzadeh

et al. 2018

2018 IEEE International Symposium on Information Theory (ISIT)

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This paper considers a generalized version of the coin weighing problem with a spring scale that lies at the intersection of group testing and compressed sensing problems. Given a collection of n ≥ 2 coins of total weight d (for a known integer d), where the weight of each coin is an unknown integer in the range of {0, 1, . . . , k} (for a known integer k ≥ 1), the problem is to determine the weight of each coin by weighing subsets of coins in a spring scale. The goal is to minimize the average number of weighings over all possible weight configurations. For d = k = 1, an adaptive bisecting weighing strategy is known to be optimal. However, even the case of d = k = 2, which is the simplest non-trivial case of the problem, is still open. For this case, we propose and analyze a simple and effective adaptive weighing strategy. A numerical evaluation of the exact recursive formulas, derived for the analysis of the proposed strategy, shows that this strategy requires about 1.365 log 2 n − 0.5 weighings on average. To the best of our knowledge, this is the first non-trivial achievable upper bound on the minimum expected required number of weighings for the case of d = k = 2. As n grows unbounded, the proposed strategy, when compared to an optimal strategy within the commonly-used class of nested strategies, requires about 31.75% less number of weighings on average; and in comparison with the information-theoretic lower bound, it requires at most about 8.16% extra number of weighings on average.

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“…There are several recent studies on noisy group testing that assume the presence of one-sided noise [15], [16] or the symmetric case with equal size-independent false alarm and miss detection probabilities [17], [18]. In some extened group testing models such as the noisy quantitative group testing [19] and threshold group testing [20], the issue of sample complexity in terms of detection accuracy is absent in the basic formulation. Similar to the group testing problem, the objective of the compressed sensing problem [15] is to recover a sparse signal with aggregated observations.…”

Section: A Noisy Group Testing and Compressed Sensingmentioning

confidence: 99%

Active hypothesis testing on a tree: Anomaly detection under hierarchical observations

Wang

Cohen

Zhao

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Abstract-The problem of detecting a few anomalous processes among a large number of data streams is considered. At each time, aggregated observations can be taken from a chosen subset of processes, where the chosen subset conforms to a given binary tree structure. The random observations are drawn from a general distribution that may depend on the size of the chosen subset and the number of anomalous processes in the subset. We propose a sequential search strategy by devising an informationdirected random walk (IRW) on the tree-structured observation hierarchy. The sample complexity of the IRW policy is shown to be asymptotically optimal in terms of detection accuracy and order optimal in terms of the number of data streams.

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Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

Cited by 18 publications

References 54 publications

Sparse Graph Codes for Non-adaptive Quantitative Group Testing

Sparse Graph Codes for Non-adaptive Quantitative Group Testing

A Simple and Efficient Strategy for the Coin Weighing Problem with a Spring Scale

Active hypothesis testing on a tree: Anomaly detection under hierarchical observations

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