Generalized framework for Group Testing: Queries, feedbacks and adversaries
In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Klonowski, Marek [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
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| Schlagwörter: |
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| Umfang: |
18 |
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| Übergeordnetes Werk: |
Enthalten in: Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries - Schweiss, Rüdiger ELSEVIER, 2015transfer abstract, the journal of the EATCS, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:919 ; year:2022 ; day:5 ; month:06 ; pages:18-35 ; extent:18 |
| Links: |
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| DOI / URN: |
10.1016/j.tcs.2022.03.026 |
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ELV057600368 |
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| 245 | 1 | 0 | |a Generalized framework for Group Testing: Queries, feedbacks and adversaries |
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| 520 | |a In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. | ||
| 520 | |a In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. | ||
| 650 | 7 | |a Adversaries |2 Elsevier | |
| 650 | 7 | |a Lower bound |2 Elsevier | |
| 650 | 7 | |a Queries |2 Elsevier | |
| 650 | 7 | |a Group testing |2 Elsevier | |
| 650 | 7 | |a Non-adaptive algorithms |2 Elsevier | |
| 650 | 7 | |a Randomized algorithms |2 Elsevier | |
| 650 | 7 | |a Feedback functions |2 Elsevier | |
| 650 | 7 | |a Deterministic algorithms |2 Elsevier | |
| 700 | 1 | |a Kowalski, Dariusz R. |4 oth | |
| 700 | 1 | |a Pająk, Dominik |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |a Schweiss, Rüdiger ELSEVIER |t Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries |d 2015transfer abstract |d the journal of the EATCS |g Amsterdam [u.a.] |w (DE-627)ELV013125583 |
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10.1016/j.tcs.2022.03.026 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001760.pica (DE-627)ELV057600368 (ELSEVIER)S0304-3975(22)00166-9 DE-627 ger DE-627 rakwb eng 620 VZ 690 VZ 50.92 bkl Klonowski, Marek verfasserin aut Generalized framework for Group Testing: Queries, feedbacks and adversaries 2022transfer abstract 18 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. Adversaries Elsevier Lower bound Elsevier Queries Elsevier Group testing Elsevier Non-adaptive algorithms Elsevier Randomized algorithms Elsevier Feedback functions Elsevier Deterministic algorithms Elsevier Kowalski, Dariusz R. oth Pająk, Dominik oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:919 year:2022 day:5 month:06 pages:18-35 extent:18 https://doi.org/10.1016/j.tcs.2022.03.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 919 2022 5 0605 18-35 18 |
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10.1016/j.tcs.2022.03.026 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001760.pica (DE-627)ELV057600368 (ELSEVIER)S0304-3975(22)00166-9 DE-627 ger DE-627 rakwb eng 620 VZ 690 VZ 50.92 bkl Klonowski, Marek verfasserin aut Generalized framework for Group Testing: Queries, feedbacks and adversaries 2022transfer abstract 18 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. Adversaries Elsevier Lower bound Elsevier Queries Elsevier Group testing Elsevier Non-adaptive algorithms Elsevier Randomized algorithms Elsevier Feedback functions Elsevier Deterministic algorithms Elsevier Kowalski, Dariusz R. oth Pająk, Dominik oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:919 year:2022 day:5 month:06 pages:18-35 extent:18 https://doi.org/10.1016/j.tcs.2022.03.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 919 2022 5 0605 18-35 18 |
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10.1016/j.tcs.2022.03.026 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001760.pica (DE-627)ELV057600368 (ELSEVIER)S0304-3975(22)00166-9 DE-627 ger DE-627 rakwb eng 620 VZ 690 VZ 50.92 bkl Klonowski, Marek verfasserin aut Generalized framework for Group Testing: Queries, feedbacks and adversaries 2022transfer abstract 18 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. Adversaries Elsevier Lower bound Elsevier Queries Elsevier Group testing Elsevier Non-adaptive algorithms Elsevier Randomized algorithms Elsevier Feedback functions Elsevier Deterministic algorithms Elsevier Kowalski, Dariusz R. oth Pająk, Dominik oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:919 year:2022 day:5 month:06 pages:18-35 extent:18 https://doi.org/10.1016/j.tcs.2022.03.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 919 2022 5 0605 18-35 18 |
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10.1016/j.tcs.2022.03.026 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001760.pica (DE-627)ELV057600368 (ELSEVIER)S0304-3975(22)00166-9 DE-627 ger DE-627 rakwb eng 620 VZ 690 VZ 50.92 bkl Klonowski, Marek verfasserin aut Generalized framework for Group Testing: Queries, feedbacks and adversaries 2022transfer abstract 18 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. Adversaries Elsevier Lower bound Elsevier Queries Elsevier Group testing Elsevier Non-adaptive algorithms Elsevier Randomized algorithms Elsevier Feedback functions Elsevier Deterministic algorithms Elsevier Kowalski, Dariusz R. oth Pająk, Dominik oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:919 year:2022 day:5 month:06 pages:18-35 extent:18 https://doi.org/10.1016/j.tcs.2022.03.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 919 2022 5 0605 18-35 18 |
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10.1016/j.tcs.2022.03.026 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001760.pica (DE-627)ELV057600368 (ELSEVIER)S0304-3975(22)00166-9 DE-627 ger DE-627 rakwb eng 620 VZ 690 VZ 50.92 bkl Klonowski, Marek verfasserin aut Generalized framework for Group Testing: Queries, feedbacks and adversaries 2022transfer abstract 18 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. Adversaries Elsevier Lower bound Elsevier Queries Elsevier Group testing Elsevier Non-adaptive algorithms Elsevier Randomized algorithms Elsevier Feedback functions Elsevier Deterministic algorithms Elsevier Kowalski, Dariusz R. oth Pająk, Dominik oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:919 year:2022 day:5 month:06 pages:18-35 extent:18 https://doi.org/10.1016/j.tcs.2022.03.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 919 2022 5 0605 18-35 18 |
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Generalized framework for Group Testing: Queries, feedbacks and adversaries |
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In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. |
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In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. |
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In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q . A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity α and output expressiveness β. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non-adaptive, deterministic Group Testing under some “efficient” feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters α , β . Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity α. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions. |
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