224,871 research outputs found
The Euclidean Algorithm for Generalized Minimum Distance Decoding of Reed-Solomon Codes
This paper presents a method to merge Generalized Minimum Distance decoding
of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean
that the steps taken to perform the Generalized Minimum Distance decoding are
similar to those performed by the extended Euclidean algorithm. The resulting
algorithm has a complexity of O(n^2)
An ETH-Tight Exact Algorithm for Euclidean TSP
We study exact algorithms for {\sc Euclidean TSP} in . In the
early 1990s algorithms with running time were presented for
the planar case, and some years later an algorithm with
running time was presented for any . Despite significant interest in
subexponential exact algorithms over the past decade, there has been no
progress on {\sc Euclidean TSP}, except for a lower bound stating that the
problem admits no algorithm unless ETH fails. Up to
constant factors in the exponent, we settle the complexity of {\sc Euclidean
TSP} by giving a algorithm and by showing that a
algorithm does not exist unless ETH fails.Comment: To appear in FOCS 201
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