Efficient Algorithms for Noisy Group Testing

Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Cai, Sheng [verfasserIn] Jahangoshahi, Mohammad Bakshi, Mayank Jaggi, Sidharth

Format:	Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	bipartite graph Decoding encoding Algorithm design and analysis greedy algorithms random variables Reconstruction algorithms Testing Complexity theory Adaptive algorithms Noise measurement error correction codes

Systematik:	SA 5570

Übergeordnetes Werk:	Enthalten in: IEEE transactions on information theory - Piscataway, NJ : IEEE, 1963, 63(2017), 4, Seite 2113-2136
Übergeordnetes Werk:	volume:63 ; year:2017 ; number:4 ; pages:2113-2136

Links:	Volltext Link aufrufen

DOI / URN:	10.1109/TIT.2017.2659619

Katalog-ID:	OLC1992036233

Internformat


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520			\|a Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements.
650		4	\|a bipartite graph
650		4	\|a Decoding
650		4	\|a encoding
650		4	\|a Algorithm design and analysis
650		4	\|a greedy algorithms
650		4	\|a random variables
650		4	\|a Reconstruction algorithms
650		4	\|a Testing
650		4	\|a Complexity theory
650		4	\|a Adaptive algorithms
650		4	\|a Noise measurement
650		4	\|a error correction codes
700	1		\|a Jahangoshahi, Mohammad \|4 oth
700	1		\|a Bakshi, Mayank \|4 oth
700	1		\|a Jaggi, Sidharth \|4 oth
773	0	8	\|i Enthalten in \|t IEEE transactions on information theory \|d Piscataway, NJ : IEEE, 1963 \|g 63(2017), 4, Seite 2113-2136 \|w (DE-627)12954731X \|w (DE-600)218505-2 \|w (DE-576)01499819X \|x 0018-9448 \|7 nnns
773	1	8	\|g volume:63 \|g year:2017 \|g number:4 \|g pages:2113-2136
856	4	1	\|u http://dx.doi.org/10.1109/TIT.2017.2659619 \|3 Volltext
856	4	2	\|u http://ieeexplore.ieee.org/document/7835117
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allfields	10.1109/TIT.2017.2659619 doi PQ20170501 (DE-627)OLC1992036233 (DE-599)GBVOLC1992036233 (PRQ)c1066-a90115a3c3080308c7c8de02c6d5d88d76b48561fe654cf7449d76df41386b0c0 (KEY)0023448620170000063000402113efficientalgorithmsfornoisygrouptesting DE-627 ger DE-627 rakwb eng 070 620 DNB SA 5570 AVZ rvk Cai, Sheng verfasserin aut Efficient Algorithms for Noisy Group Testing 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements. bipartite graph Decoding encoding Algorithm design and analysis greedy algorithms random variables Reconstruction algorithms Testing Complexity theory Adaptive algorithms Noise measurement error correction codes Jahangoshahi, Mohammad oth Bakshi, Mayank oth Jaggi, Sidharth oth Enthalten in IEEE transactions on information theory Piscataway, NJ : IEEE, 1963 63(2017), 4, Seite 2113-2136 (DE-627)12954731X (DE-600)218505-2 (DE-576)01499819X 0018-9448 nnns volume:63 year:2017 number:4 pages:2113-2136 http://dx.doi.org/10.1109/TIT.2017.2659619 Volltext http://ieeexplore.ieee.org/document/7835117 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OLC-BUB SSG-OPC-BBI GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 SA 5570 AR 63 2017 4 2113-2136
spelling	10.1109/TIT.2017.2659619 doi PQ20170501 (DE-627)OLC1992036233 (DE-599)GBVOLC1992036233 (PRQ)c1066-a90115a3c3080308c7c8de02c6d5d88d76b48561fe654cf7449d76df41386b0c0 (KEY)0023448620170000063000402113efficientalgorithmsfornoisygrouptesting DE-627 ger DE-627 rakwb eng 070 620 DNB SA 5570 AVZ rvk Cai, Sheng verfasserin aut Efficient Algorithms for Noisy Group Testing 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements. bipartite graph Decoding encoding Algorithm design and analysis greedy algorithms random variables Reconstruction algorithms Testing Complexity theory Adaptive algorithms Noise measurement error correction codes Jahangoshahi, Mohammad oth Bakshi, Mayank oth Jaggi, Sidharth oth Enthalten in IEEE transactions on information theory Piscataway, NJ : IEEE, 1963 63(2017), 4, Seite 2113-2136 (DE-627)12954731X (DE-600)218505-2 (DE-576)01499819X 0018-9448 nnns volume:63 year:2017 number:4 pages:2113-2136 http://dx.doi.org/10.1109/TIT.2017.2659619 Volltext http://ieeexplore.ieee.org/document/7835117 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OLC-BUB SSG-OPC-BBI GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 SA 5570 AR 63 2017 4 2113-2136
allfields_unstemmed	10.1109/TIT.2017.2659619 doi PQ20170501 (DE-627)OLC1992036233 (DE-599)GBVOLC1992036233 (PRQ)c1066-a90115a3c3080308c7c8de02c6d5d88d76b48561fe654cf7449d76df41386b0c0 (KEY)0023448620170000063000402113efficientalgorithmsfornoisygrouptesting DE-627 ger DE-627 rakwb eng 070 620 DNB SA 5570 AVZ rvk Cai, Sheng verfasserin aut Efficient Algorithms for Noisy Group Testing 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements. bipartite graph Decoding encoding Algorithm design and analysis greedy algorithms random variables Reconstruction algorithms Testing Complexity theory Adaptive algorithms Noise measurement error correction codes Jahangoshahi, Mohammad oth Bakshi, Mayank oth Jaggi, Sidharth oth Enthalten in IEEE transactions on information theory Piscataway, NJ : IEEE, 1963 63(2017), 4, Seite 2113-2136 (DE-627)12954731X (DE-600)218505-2 (DE-576)01499819X 0018-9448 nnns volume:63 year:2017 number:4 pages:2113-2136 http://dx.doi.org/10.1109/TIT.2017.2659619 Volltext http://ieeexplore.ieee.org/document/7835117 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OLC-BUB SSG-OPC-BBI GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 SA 5570 AR 63 2017 4 2113-2136
allfieldsGer	10.1109/TIT.2017.2659619 doi PQ20170501 (DE-627)OLC1992036233 (DE-599)GBVOLC1992036233 (PRQ)c1066-a90115a3c3080308c7c8de02c6d5d88d76b48561fe654cf7449d76df41386b0c0 (KEY)0023448620170000063000402113efficientalgorithmsfornoisygrouptesting DE-627 ger DE-627 rakwb eng 070 620 DNB SA 5570 AVZ rvk Cai, Sheng verfasserin aut Efficient Algorithms for Noisy Group Testing 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements. bipartite graph Decoding encoding Algorithm design and analysis greedy algorithms random variables Reconstruction algorithms Testing Complexity theory Adaptive algorithms Noise measurement error correction codes Jahangoshahi, Mohammad oth Bakshi, Mayank oth Jaggi, Sidharth oth Enthalten in IEEE transactions on information theory Piscataway, NJ : IEEE, 1963 63(2017), 4, Seite 2113-2136 (DE-627)12954731X (DE-600)218505-2 (DE-576)01499819X 0018-9448 nnns volume:63 year:2017 number:4 pages:2113-2136 http://dx.doi.org/10.1109/TIT.2017.2659619 Volltext http://ieeexplore.ieee.org/document/7835117 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OLC-BUB SSG-OPC-BBI GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 SA 5570 AR 63 2017 4 2113-2136
allfieldsSound	10.1109/TIT.2017.2659619 doi PQ20170501 (DE-627)OLC1992036233 (DE-599)GBVOLC1992036233 (PRQ)c1066-a90115a3c3080308c7c8de02c6d5d88d76b48561fe654cf7449d76df41386b0c0 (KEY)0023448620170000063000402113efficientalgorithmsfornoisygrouptesting DE-627 ger DE-627 rakwb eng 070 620 DNB SA 5570 AVZ rvk Cai, Sheng verfasserin aut Efficient Algorithms for Noisy Group Testing 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements. bipartite graph Decoding encoding Algorithm design and analysis greedy algorithms random variables Reconstruction algorithms Testing Complexity theory Adaptive algorithms Noise measurement error correction codes Jahangoshahi, Mohammad oth Bakshi, Mayank oth Jaggi, Sidharth oth Enthalten in IEEE transactions on information theory Piscataway, NJ : IEEE, 1963 63(2017), 4, Seite 2113-2136 (DE-627)12954731X (DE-600)218505-2 (DE-576)01499819X 0018-9448 nnns volume:63 year:2017 number:4 pages:2113-2136 http://dx.doi.org/10.1109/TIT.2017.2659619 Volltext http://ieeexplore.ieee.org/document/7835117 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OLC-BUB SSG-OPC-BBI GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 SA 5570 AR 63 2017 4 2113-2136
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source	Enthalten in IEEE transactions on information theory 63(2017), 4, Seite 2113-2136 volume:63 year:2017 number:4 pages:2113-2136
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institution	findex.gbv.de
topic_facet	bipartite graph Decoding encoding Algorithm design and analysis greedy algorithms random variables Reconstruction algorithms Testing Complexity theory Adaptive algorithms Noise measurement error correction codes
dewey-raw	070
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authorswithroles_txt_mv	Cai, Sheng @@aut@@ Jahangoshahi, Mohammad @@oth@@ Bakshi, Mayank @@oth@@ Jaggi, Sidharth @@oth@@
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author	Cai, Sheng
spellingShingle	Cai, Sheng ddc 070 rvk SA 5570 misc bipartite graph misc Decoding misc encoding misc Algorithm design and analysis misc greedy algorithms misc random variables misc Reconstruction algorithms misc Testing misc Complexity theory misc Adaptive algorithms misc Noise measurement misc error correction codes Efficient Algorithms for Noisy Group Testing
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title	Efficient Algorithms for Noisy Group Testing
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title_sort	efficient algorithms for noisy group testing
title_auth	Efficient Algorithms for Noisy Group Testing
abstract	Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements.
abstractGer	Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements.
abstract_unstemmed	Group-testing refers to the problem of identifying (with high probability) a (small) subset of <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> defectives from a (large) set of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> items via a "small" number of "pooled" tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when <inline-formula> <tex-math notation="LaTeX">D = \mathcal {O}(N^{1- {\delta }}) </tex-math></inline-formula> for some <inline-formula> <tex-math notation="LaTeX"> {\delta }> 0 </tex-math></inline-formula>. The tests may be noiseless or noisy , and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of the literature demonstrates that <inline-formula> <tex-math notation="LaTeX">\Theta (D\log (N)) </tex-math></inline-formula> tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexities that are sub-linear in <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> have started being investigated. In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (N)}\right ) </tex-math></inline-formula> in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (<inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({\log (D)}\right ) </tex-math></inline-formula>). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({D\log (D)\log (N)}\right ) </tex-math></inline-formula> tests and has a decoding complexity of <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. Finally, we present an adaptive algorithm that only requires two stages, and for which both the number of tests and the decoding complexity scale as <inline-formula> <tex-math notation="LaTeX">{\mathcal{ O}}(D(\log N+\log ^{2}D)) </tex-math></inline-formula>. For all three settings, the probability of error of our algorithms scales as <inline-formula> <tex-math notation="LaTeX"> \mathcal {O}\left ({1/(poly(D)}\right ) </tex-math></inline-formula>. For each of the statements mentioned earlier about the order of the number of measurements, decoding complexity, and probability of error, we provide explicitly computed "small" universal factors in our theorem statements.
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container_issue	4
title_short	Efficient Algorithms for Noisy Group Testing
url	http://dx.doi.org/10.1109/TIT.2017.2659619 http://ieeexplore.ieee.org/document/7835117
remote_bool	false
author2	Jahangoshahi, Mohammad Bakshi, Mayank Jaggi, Sidharth
author2Str	Jahangoshahi, Mohammad Bakshi, Mayank Jaggi, Sidharth
ppnlink	12954731X
mediatype_str_mv	n
isOA_txt	false
hochschulschrift_bool	false
author2_role	oth oth oth
doi_str	10.1109/TIT.2017.2659619
up_date	2024-07-04T04:08:05.804Z
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