Yes, that indeed is a proof. Specifically they show that k-median in the plane is NP-hard, by a very complicated reduction from 3SAT.

thanks !

]]>N. Megiddo and K. Supowit.

On the complexity of some common geometric location problems.

SIAM J Computing, 13(1), 1984.

Having never written for the CRC, I cannot say if this is true. Maybe others with experience can add to this ?

]]>Doesn’t this depend on the author more than the publishing company?

]]>If interested, can visit the blog with useful information on Car AA insurance.

]]>As far as the hardness goes, it is known that the doubly exponential dependence is (likely) necessary for a PTAS, *if* your medians must come from a given set (the “discrete median” case). This follows from a combination of papers, incl. Trevisan’97, see comments in Guruswami-Indyk, SODA’03.

So in particular, it is known that there is no PTAS for the discrete k-median in general Euclidean spaces (unless something strange happens)

Piotr

]]>I have a related question. What exactly is *the k-variance problem* ? I came across couple of different definitions. Is it’s complexity open ? Are there any known results for k-variance on euclidean plane.