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K-nearest neighbhors on an equispaced multidimensional grid


hi,

i am looking for an algorithm/data structure to find the K-nearest
neighbors on an equispaced multidimensional grid.

x=(x_1,...,x_D) where x_d takes values in (...,-1,0,1,...)  for all
d=1,...,D

for example if D=2 and x=(0,0) the

1-NN is x itself
5-NN are x, (-1,0), (0,-1),(1,0),(0,1)
9-NN are x, (-1,0), (0,-1),(1,0),(0,1),(-1,-1),(-1,1),(1,-1),(1,1)

etc...

thanks,

e.


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