Matches in SemOpenAlex for { <https://semopenalex.org/work/W2000333212> ?p ?o ?g. }
- W2000333212 endingPage "121" @default.
- W2000333212 startingPage "90" @default.
- W2000333212 abstract "We initiate the study of the computational complexity of the covering radius problem for lattices, and approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices. For the covering radius on n-dimensional lattices, we show that the problem can be approximated within any constant factor γ(n) > 1 in random exponential time 2 O(n). We also prove that suitably defined gap versions of the problem lie in AM for λ(n) = 2, in coAM for $$ gamma (n) = {sqrt {n/log n} }, $$ and in NP ∩ coNP for $$ gamma (n) = {sqrt n }. $$ For the covering radius on n-dimensional linear codes, we show that the problem can be solved in deterministic polynomial time for approximation factor $$ gamma (n) = log n, $$ but cannot be solved in polynomial time for some $$ gamma (n) = Omega (log log n) $$ unless NP can be simulated in deterministic $$ n^{{O(log log log n)}} $$ time. Moreover, we prove that the problem is NP-hard for any constant approximation factor, it is Π2-hard for some constant approximation factor, and that it is unlikely to be Π2-hard for approximation factors larger than 2 (by giving an AM protocol for the appropriate gap problem). This is a natural hardness of approximation result in the polynomial hierarchy. For the shortest independent vectors problem, we give a coAM protocol achieving approximation factor $$ gamma (n) = {sqrt {n/log n} }, $$ solving an open problem of Blömer and Seifert (STOC’99), and prove that the problem is also in coNP for $$ gamma (n) = {sqrt n }. $$ Both results are obtained by giving a gap-preserving nondeterministic polynomial time reduction to the closest vector problem." @default.
- W2000333212 created "2016-06-24" @default.
- W2000333212 creator A5023640008 @default.
- W2000333212 creator A5049700941 @default.
- W2000333212 creator A5068388812 @default.
- W2000333212 date "2005-06-01" @default.
- W2000333212 modified "2023-09-28" @default.
- W2000333212 title "The complexity of the covering radius problem" @default.
- W2000333212 cites W1485280854 @default.
- W2000333212 cites W1496447390 @default.
- W2000333212 cites W1970259241 @default.
- W2000333212 cites W1982051149 @default.
- W2000333212 cites W1989510734 @default.
- W2000333212 cites W1995990042 @default.
- W2000333212 cites W1998732904 @default.
- W2000333212 cites W2001093624 @default.
- W2000333212 cites W2001663593 @default.
- W2000333212 cites W2011039300 @default.
- W2000333212 cites W2012589104 @default.
- W2000333212 cites W2013794527 @default.
- W2000333212 cites W2046896701 @default.
- W2000333212 cites W2050689197 @default.
- W2000333212 cites W2051176401 @default.
- W2000333212 cites W2056492141 @default.
- W2000333212 cites W2059453880 @default.
- W2000333212 cites W2065251436 @default.
- W2000333212 cites W2077202644 @default.
- W2000333212 cites W2077595184 @default.
- W2000333212 cites W2092017668 @default.
- W2000333212 cites W2097678797 @default.
- W2000333212 cites W2111416661 @default.
- W2000333212 cites W2143996311 @default.
- W2000333212 cites W2144593761 @default.
- W2000333212 cites W2157396841 @default.
- W2000333212 cites W2169665116 @default.
- W2000333212 cites W2169690324 @default.
- W2000333212 cites W3014312596 @default.
- W2000333212 cites W3217775779 @default.
- W2000333212 cites W1525605957 @default.
- W2000333212 doi "https://doi.org/10.1007/s00037-005-0193-y" @default.
- W2000333212 hasPublicationYear "2005" @default.
- W2000333212 type Work @default.
- W2000333212 sameAs 2000333212 @default.
- W2000333212 citedByCount "58" @default.
- W2000333212 countsByYear W20003332122012 @default.
- W2000333212 countsByYear W20003332122013 @default.
- W2000333212 countsByYear W20003332122014 @default.
- W2000333212 countsByYear W20003332122015 @default.
- W2000333212 countsByYear W20003332122016 @default.
- W2000333212 countsByYear W20003332122017 @default.
- W2000333212 countsByYear W20003332122018 @default.
- W2000333212 countsByYear W20003332122019 @default.
- W2000333212 countsByYear W20003332122020 @default.
- W2000333212 countsByYear W20003332122021 @default.
- W2000333212 countsByYear W20003332122022 @default.
- W2000333212 crossrefType "journal-article" @default.
- W2000333212 hasAuthorship W2000333212A5023640008 @default.
- W2000333212 hasAuthorship W2000333212A5049700941 @default.
- W2000333212 hasAuthorship W2000333212A5068388812 @default.
- W2000333212 hasBestOaLocation W20003332121 @default.
- W2000333212 hasConcept C112955886 @default.
- W2000333212 hasConcept C11413529 @default.
- W2000333212 hasConcept C114614502 @default.
- W2000333212 hasConcept C118615104 @default.
- W2000333212 hasConcept C121332964 @default.
- W2000333212 hasConcept C134306372 @default.
- W2000333212 hasConcept C148764684 @default.
- W2000333212 hasConcept C178635117 @default.
- W2000333212 hasConcept C179799912 @default.
- W2000333212 hasConcept C199360897 @default.
- W2000333212 hasConcept C2777027219 @default.
- W2000333212 hasConcept C2779557605 @default.
- W2000333212 hasConcept C311688 @default.
- W2000333212 hasConcept C33923547 @default.
- W2000333212 hasConcept C38652104 @default.
- W2000333212 hasConcept C41008148 @default.
- W2000333212 hasConcept C62520636 @default.
- W2000333212 hasConcept C63553672 @default.
- W2000333212 hasConcept C71017364 @default.
- W2000333212 hasConcept C90119067 @default.
- W2000333212 hasConceptScore W2000333212C112955886 @default.
- W2000333212 hasConceptScore W2000333212C11413529 @default.
- W2000333212 hasConceptScore W2000333212C114614502 @default.
- W2000333212 hasConceptScore W2000333212C118615104 @default.
- W2000333212 hasConceptScore W2000333212C121332964 @default.
- W2000333212 hasConceptScore W2000333212C134306372 @default.
- W2000333212 hasConceptScore W2000333212C148764684 @default.
- W2000333212 hasConceptScore W2000333212C178635117 @default.
- W2000333212 hasConceptScore W2000333212C179799912 @default.
- W2000333212 hasConceptScore W2000333212C199360897 @default.
- W2000333212 hasConceptScore W2000333212C2777027219 @default.
- W2000333212 hasConceptScore W2000333212C2779557605 @default.
- W2000333212 hasConceptScore W2000333212C311688 @default.
- W2000333212 hasConceptScore W2000333212C33923547 @default.
- W2000333212 hasConceptScore W2000333212C38652104 @default.
- W2000333212 hasConceptScore W2000333212C41008148 @default.
- W2000333212 hasConceptScore W2000333212C62520636 @default.
- W2000333212 hasConceptScore W2000333212C63553672 @default.