We consider the problem of finding the closest lattice point to a vector in n-dimensional Euclidean space when each component of the vector is available at a distinct node in a network. Our objectives are (i) minimize the communication cost and (ii) obtain the error probability. The approximate closest lattice point considered here is the one obtained using the nearest-plane (Babai) algorithm. ...

We report (to our knowledge) the first evaluation of Constraint Satisfaction as a computational framework for solving closest string problems. We show that careful consideration of symbol occurrences can provide search heuristics that provide several orders of magnitude speedup at and above the optimal distance. We also report (to our knowledge) the first analysis and evaluation – using any tec...

A central problem in the algorithmic study of lattices is the closest vector problem: given a lattice L represented by some basis, and a target point y, nd the lattice point closest to y. Bounded Distance Decoding is a variant of this problem in which the target is guaranteed to be close to the lattice, relative to the minimum distance 1(L) of the lattice. Speci cally, in the -Bounded Distance ...

In an earlier paper the authors described a very fast method which, for the root lattices A,, D,, E,,, their duals and certain other lattices, finds the closest lattice point to an arbitrary point of the underlying space. If the lattices are used as codes for a Gaussian channel, the algorithm provides a fast decoding procedure, or if they are used as vector quantizers the algorithm performs the...

In this thesis we prove intractability results for several well studied problems in combinatorial optimization. Closest Vector Problem with Pre-processing (CVPP): We show that the pre-processing version of the well known Closest Vector Problem is hard to approximate to an almost polynomial factor (2 1− ) unless NP is in quasi polynomial time. The approximability of CVPP is closely related to th...

Resumen—Los algoritmos para la reducción de la base de un retículo se han convertido en una herramienta imprescindible en el criptoanálisis de muchos sistemas de cifrado y en problemas de computación en Teoría de Números. En este trabajo se describe sucintamente el problema de la reducción de base y los problemas relacionados como la búsqueda del vector más corto de un retículo (SVP, Shortest V...