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APPROX
2009
Springer

Deterministic Approximation Algorithms for the Nearest Codeword Problem

10 years 8 months ago
Deterministic Approximation Algorithms for the Nearest Codeword Problem
The Nearest Codeword Problem (NCP) is a basic algorithmic question in the theory of error-correcting codes. Given a point v ∈ Fn 2 and a linear space L ⊆ Fn 2 of dimension k NCP asks to find a point l ∈ L that minimizes the (Hamming) distance from v. It is well-known that the nearest codeword problem is NP-hard. Therefore approximation algorithms are of interest. The best efficient approximation algorithms for the NCP to date are due to Berman and Karpinski. They are a deterministic algorithm that achieves an approximation ratio of O(k/c) for an arbitrary constant c, and a randomized algorithm that achieves an approximation ratio of O(k/ log n). In this paper we present new deterministic algorithms for approximating the NCP that improve substantially upon the earlier work. Specifically, we obtain: – A polynomial time O(n/ log n)-approximation algorithm; – An nO(s) time O(k log(s) n/ log n)-approximation algorithm, where log(s) n stands for s iterations of log, e.g., log(2) ...
Noga Alon, Rina Panigrahy, Sergey Yekhanin
Added 25 May 2010
Updated 25 May 2010
Type Conference
Year 2009
Where APPROX
Authors Noga Alon, Rina Panigrahy, Sergey Yekhanin
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