TY  - RPRT
A1  - Rössner, Carsten
A1  - Seifert, Jean-Pierre
T1  - Approximating good simultaneous diophantine approximations is almost NP-hard
N2  - Given a real vector alpha =(alpha1 ; : : : ; alpha d ) and a real number E > 0 a good Diophantine approximation to alpha is a number Q such that IIQ alpha mod Zk1 ", where k \Delta k1 denotes the 1-norm kxk1 := max 1id jx i j for x = (x1 ; : : : ; xd ). Lagarias [12] proved the NP-completeness of the corresponding decision problem, i.e., given a vector ff 2 Q d , a rational number " ? 0 and a number N 2 N+ , decide whether there exists a number Q with 1 Q N and kQff mod Zk1 ". We prove that, unless ...
Y1  - 2005
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/4240
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30-12498
N1  - auch in: 21st International Symposium on Mathematical Foundations of Computer Science (MFCS '96); Lecture Notes in Computer Science, Springer-Verlag, 1996
ER  -