Optimal Partitions

Hwang, F. K.; Rothblum, Uriel G.

doi:10.1007/978-1-4419-7997-1_40

Cited by 3 publications

(4 citation statements)

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“…In general, an optimum partition problem is a hard computational problem. This is why the optimal solution for the generalized group testing problem is only available for the Dorfman procedure (Hwang, 1975(Hwang, , 1981. In this work we try to shed light on the additional procedures.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…solution can be obtained with polynomial in N computation cost (see, e.g., Hwang (1975); Tanaev (1979); Hwang (1981); Chakravarty et al (1982)).…”

Section: Introductionmentioning

confidence: 99%

“…In the group-testing setting, Hwang (1975Hwang ( , 1981 proved that under procedure D an optimal partition is an ordered partition (i.e., each pair of subsets has the property that the numbers in one subset are all great or equal to every number in the other subset). The total number of ordered partition of a set of size N is 2 N −1 .…”

Section: Introductionmentioning

confidence: 99%

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Sterrett Procedure for the Generalized Group Testing Problem

Malinovsky

2017

Methodol Comput Appl Probab

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Group testing is a useful method that has broad applications in medicine, engineering, and even in airport security control. Consider a finite population of N items, where item i has a probability p i to be defective. The goal is to identify all items by means of group testing. This is the generalized group testing problem. The optimum procedure, with respect to the expected total number of tests, is unknown even in case when all p i are equal. Hwang (1975) proved that an ordered partition (with respect to p i ) is the optimal for the Dorfman procedure (procedure D), and obtained an optimum solution (i.e., found an optimal partition) by dynamic programming. In this paper, we investigate the Sterrett procedure (procedure S). We provide close form expression for the expected total number of tests, which allows us to find the optimum arrangement of the items in the particular group. We also show that an ordered partition is not optimal for the procedure S or even for a slightly modified Dorfman procedure (procedure D ′ ). This discovery implies that finding an optimal procedure S appears to be a hard computational problem. However, by using an optimal ordered partition for all procedures, we show that procedure D ′ is uniformly better than procedure D, and based on numerical comparisons, procedure S is uniformly and significantly better than procedures D and D ′ .

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Section: Conclusion and Discussionmentioning

confidence: 99%

“…solution can be obtained with polynomial in N computation cost (see, e.g., Hwang (1975); Tanaev (1979); Hwang (1981); Chakravarty et al (1982)).…”

Section: Introductionmentioning

confidence: 99%

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Sterrett Procedure for the Generalized Group Testing Problem

Malinovsky

2017

Methodol Comput Appl Probab

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“…, which grows exponentially with N. For example, B(13) = 27, 644, 437. In fact, the optimal partition is known only for Procedure D, due to Hwang (1975Hwang ( , 1981. Hwang proved that under Procedure D, an optimal partition is an ordered partition (i.e.…”

Section: Dorfman and Sterrett Proceduresmentioning

confidence: 99%

Nested Group Testing Procedures for Screening

Malinovsky¹,

Albert²

2021

Preprint

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This article reviews a class of adaptive group testing procedures that operate under a probabilistic model assumption as follows. Consider a set of N items, where item i has the probability p (p i in the generalized group testing) to be defective, and the probability 1 − p to be non-defective independent from the other items. A group test applied to any subset of size n is a binary test with two possible outcomes, positive or negative. The outcome is negative if all n items are non-defective, whereas the outcome is positive if at least one item among the n items is defective. The goal is complete identification of all N items with the minimum expected number of tests.

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