Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing
Abstract Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We...
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Gespeichert in:
| Autor*in: |
De Bonis, Annalisa [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of combinatorial optimization - Springer US, 1997, 32(2015), 4 vom: 04. Sept., Seite 1254-1287 |
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| Übergeordnetes Werk: |
volume:32 ; year:2015 ; number:4 ; day:04 ; month:09 ; pages:1254-1287 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10878-015-9949-8 |
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OLC2044621053 |
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| 520 | |a Abstract Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of “yes” responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of “yes” responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our two-stage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of “yes” responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p, d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts. | ||
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10.1007/s10878-015-9949-8 doi (DE-627)OLC2044621053 (DE-He213)s10878-015-9949-8-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn De Bonis, Annalisa verfasserin aut Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of “yes” responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of “yes” responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our two-stage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of “yes” responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p, d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts. Group testing Cover free families Adaptive algorithms Non adaptive algorithms Two-stage algorithms Enthalten in Journal of combinatorial optimization Springer US, 1997 32(2015), 4 vom: 04. Sept., Seite 1254-1287 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:32 year:2015 number:4 day:04 month:09 pages:1254-1287 https://doi.org/10.1007/s10878-015-9949-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2108 AR 32 2015 4 04 09 1254-1287 |
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10.1007/s10878-015-9949-8 doi (DE-627)OLC2044621053 (DE-He213)s10878-015-9949-8-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn De Bonis, Annalisa verfasserin aut Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of “yes” responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of “yes” responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our two-stage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of “yes” responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p, d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts. Group testing Cover free families Adaptive algorithms Non adaptive algorithms Two-stage algorithms Enthalten in Journal of combinatorial optimization Springer US, 1997 32(2015), 4 vom: 04. Sept., Seite 1254-1287 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:32 year:2015 number:4 day:04 month:09 pages:1254-1287 https://doi.org/10.1007/s10878-015-9949-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2108 AR 32 2015 4 04 09 1254-1287 |
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10.1007/s10878-015-9949-8 doi (DE-627)OLC2044621053 (DE-He213)s10878-015-9949-8-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn De Bonis, Annalisa verfasserin aut Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of “yes” responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of “yes” responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our two-stage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of “yes” responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p, d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts. Group testing Cover free families Adaptive algorithms Non adaptive algorithms Two-stage algorithms Enthalten in Journal of combinatorial optimization Springer US, 1997 32(2015), 4 vom: 04. Sept., Seite 1254-1287 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:32 year:2015 number:4 day:04 month:09 pages:1254-1287 https://doi.org/10.1007/s10878-015-9949-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2108 AR 32 2015 4 04 09 1254-1287 |
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Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing |
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Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing |
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De Bonis, Annalisa |
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Journal of combinatorial optimization |
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Journal of combinatorial optimization |
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De Bonis, Annalisa |
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10.1007/s10878-015-9949-8 |
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constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing |
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Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing |
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Abstract Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of “yes” responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of “yes” responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our two-stage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of “yes” responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p, d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts. © Springer Science+Business Media New York 2015 |
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Abstract Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of “yes” responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of “yes” responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our two-stage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of “yes” responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p, d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts. © Springer Science+Business Media New York 2015 |
| abstract_unstemmed |
Abstract Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of “yes” responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of “yes” responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our two-stage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of “yes” responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p, d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts. © Springer Science+Business Media New York 2015 |
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Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing |
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