Information Lower Bounds via Self-Reducibility
Abstract We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Braverman, Mark [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| 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: Theory of computing systems - Springer US, 1997, 59(2015), 2 vom: 24. Sept., Seite 377-396 |
|---|---|
| Übergeordnetes Werk: |
volume:59 ; year:2015 ; number:2 ; day:24 ; month:09 ; pages:377-396 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00224-015-9655-z |
|---|
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OLC2061923089 |
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| 520 | |a Abstract We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the Ω(n) bound recently shown by Kerenidis et al. (2012), and answers an open problem from Chakrabarti et al. (2012). In our second result we prove that the information cost of IPn is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the Ω(n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 2011). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. 2001; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702–732 2004; Barak et al. 2010) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. | ||
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10.1007/s00224-015-9655-z doi (DE-627)OLC2061923089 (DE-He213)s00224-015-9655-z-p DE-627 ger DE-627 rakwb eng 004 510 VZ 510 000 VZ Braverman, Mark verfasserin aut Information Lower Bounds via Self-Reducibility 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the Ω(n) bound recently shown by Kerenidis et al. (2012), and answers an open problem from Chakrabarti et al. (2012). In our second result we prove that the information cost of IPn is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the Ω(n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 2011). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. 2001; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702–732 2004; Barak et al. 2010) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. Information complexity Communication complexity Self-reducibility Gap-hamming distance Inner product Garg, Ankit aut Pankratov, Denis aut Weinstein, Omri aut Enthalten in Theory of computing systems Springer US, 1997 59(2015), 2 vom: 24. Sept., Seite 377-396 (DE-627)222610387 (DE-600)1355722-1 (DE-576)056755198 1432-4350 nnns volume:59 year:2015 number:2 day:24 month:09 pages:377-396 https://doi.org/10.1007/s00224-015-9655-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-BUB SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4318 GBV_ILN_4319 AR 59 2015 2 24 09 377-396 |
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10.1007/s00224-015-9655-z doi (DE-627)OLC2061923089 (DE-He213)s00224-015-9655-z-p DE-627 ger DE-627 rakwb eng 004 510 VZ 510 000 VZ Braverman, Mark verfasserin aut Information Lower Bounds via Self-Reducibility 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the Ω(n) bound recently shown by Kerenidis et al. (2012), and answers an open problem from Chakrabarti et al. (2012). In our second result we prove that the information cost of IPn is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the Ω(n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 2011). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. 2001; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702–732 2004; Barak et al. 2010) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. Information complexity Communication complexity Self-reducibility Gap-hamming distance Inner product Garg, Ankit aut Pankratov, Denis aut Weinstein, Omri aut Enthalten in Theory of computing systems Springer US, 1997 59(2015), 2 vom: 24. Sept., Seite 377-396 (DE-627)222610387 (DE-600)1355722-1 (DE-576)056755198 1432-4350 nnns volume:59 year:2015 number:2 day:24 month:09 pages:377-396 https://doi.org/10.1007/s00224-015-9655-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-BUB SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4318 GBV_ILN_4319 AR 59 2015 2 24 09 377-396 |
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Information Lower Bounds via Self-Reducibility |
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Information Lower Bounds via Self-Reducibility |
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Braverman, Mark |
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Braverman, Mark Garg, Ankit Pankratov, Denis Weinstein, Omri |
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information lower bounds via self-reducibility |
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Information Lower Bounds via Self-Reducibility |
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Abstract We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the Ω(n) bound recently shown by Kerenidis et al. (2012), and answers an open problem from Chakrabarti et al. (2012). In our second result we prove that the information cost of IPn is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the Ω(n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 2011). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. 2001; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702–732 2004; Barak et al. 2010) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. © Springer Science+Business Media New York 2015 |
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Abstract We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the Ω(n) bound recently shown by Kerenidis et al. (2012), and answers an open problem from Chakrabarti et al. (2012). In our second result we prove that the information cost of IPn is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the Ω(n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 2011). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. 2001; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702–732 2004; Barak et al. 2010) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. © Springer Science+Business Media New York 2015 |
| abstract_unstemmed |
Abstract We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the Ω(n) bound recently shown by Kerenidis et al. (2012), and answers an open problem from Chakrabarti et al. (2012). In our second result we prove that the information cost of IPn is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the Ω(n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 2011). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. 2001; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702–732 2004; Barak et al. 2010) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. © Springer Science+Business Media New York 2015 |
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