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Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms

Bibliographic Details
Main Author: Bennett, Huck
Publication Date: 2023
Other Authors: Cheraghchi, Mahdi, Guruswami, Venkatesan, Ribeiro, João
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10362/158300
Summary: Funding Information: M. Cheraghchi’s research was partially supported by the National Science Foundation under Grants No. CCF-2006455 and CCF-2107345. V. Guruswami’s research was supported in part by NSF grants CCF-2228287 and CCF-2210823 and a Simons Investigator award. J. Ribeiro’s research was supported by NOVA LINCS (UIDB/04516/2020) with the financial support of FCT - Fundação para a Ciência e a Tecnologia and by the NSF grants CCF-1814603 and CCF-2107347 and the following grants of Vipul Goyal: the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award. Publisher Copyright: © 2023 ACM.
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spelling Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNormsApproximationMinimum Distance ProblemParameterized hardnessShortest Vector ProblemSoftwareFunding Information: M. Cheraghchi’s research was partially supported by the National Science Foundation under Grants No. CCF-2006455 and CCF-2107345. V. Guruswami’s research was supported in part by NSF grants CCF-2228287 and CCF-2210823 and a Simons Investigator award. J. Ribeiro’s research was supported by NOVA LINCS (UIDB/04516/2020) with the financial support of FCT - Fundação para a Ciência e a Tecnologia and by the NSF grants CCF-1814603 and CCF-2107347 and the following grants of Vipul Goyal: the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award. Publisher Copyright: © 2023 ACM.We prove that the Minimum Distance Problem (MDP) on linear codes over any fixed finite field and parameterized by the input distance bound is W[1]-hard to approximate within any constant factor. We also prove analogous results for the parameterized Shortest Vector Problem (SVP) on integer lattices. Specifically, we prove that SVP in the p norm is W[1]-hard to approximate within any constant factor for any fixed p >1 and W[1]-hard to approximate within a factor approaching 2 for p=1. (We show hardness under randomized reductions in each case.) These results answer the main questions left open (and explicitly posed) by Bhattacharyya, Bonnet, Egri, Ghoshal, Karthik C. S., Lin, Manurangsi, and Marx (Journal of the ACM, 2021) on the complexity of parameterized MDP and SVP. For MDP, they established similar hardness for binary linear codes and left the case of general fields open. For SVP in p norms with p > 1, they showed inapproximability within some constant factor (depending on p) and left open showing such hardness for arbitrary constant factors. They also left open showing W[1]-hardness even of exact SVP in the 1 norm.ACM - Association for Computing MachineryNOVALincsRUNBennett, HuckCheraghchi, MahdiGuruswami, VenkatesanRibeiro, João2023-09-26T22:13:06Z2023-06-022023-06-02T00:00:00Zconference objectinfo:eu-repo/semantics/publishedVersion14application/pdfhttp://hdl.handle.net/10362/158300eng97814503991350737-8017PURE: 72478252https://doi.org/10.1145/3564246.3585214info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-22T18:14:39Zoai:run.unl.pt:10362/158300Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T17:45:12.347294Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms
title Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms
spellingShingle Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms
Bennett, Huck
Approximation
Minimum Distance Problem
Parameterized hardness
Shortest Vector Problem
Software
title_short Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms
title_full Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms
title_fullStr Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms
title_full_unstemmed Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms
title_sort Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓpNorms
author Bennett, Huck
author_facet Bennett, Huck
Cheraghchi, Mahdi
Guruswami, Venkatesan
Ribeiro, João
author_role author
author2 Cheraghchi, Mahdi
Guruswami, Venkatesan
Ribeiro, João
author2_role author
author
author
dc.contributor.none.fl_str_mv NOVALincs
RUN
dc.contributor.author.fl_str_mv Bennett, Huck
Cheraghchi, Mahdi
Guruswami, Venkatesan
Ribeiro, João
dc.subject.por.fl_str_mv Approximation
Minimum Distance Problem
Parameterized hardness
Shortest Vector Problem
Software
topic Approximation
Minimum Distance Problem
Parameterized hardness
Shortest Vector Problem
Software
description Funding Information: M. Cheraghchi’s research was partially supported by the National Science Foundation under Grants No. CCF-2006455 and CCF-2107345. V. Guruswami’s research was supported in part by NSF grants CCF-2228287 and CCF-2210823 and a Simons Investigator award. J. Ribeiro’s research was supported by NOVA LINCS (UIDB/04516/2020) with the financial support of FCT - Fundação para a Ciência e a Tecnologia and by the NSF grants CCF-1814603 and CCF-2107347 and the following grants of Vipul Goyal: the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award. Publisher Copyright: © 2023 ACM.
publishDate 2023
dc.date.none.fl_str_mv 2023-09-26T22:13:06Z
2023-06-02
2023-06-02T00:00:00Z
dc.type.driver.fl_str_mv conference object
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/158300
url http://hdl.handle.net/10362/158300
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 9781450399135
0737-8017
PURE: 72478252
https://doi.org/10.1145/3564246.3585214
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 14
application/pdf
dc.publisher.none.fl_str_mv ACM - Association for Computing Machinery
publisher.none.fl_str_mv ACM - Association for Computing Machinery
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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