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Given $A\in\Bbb Z^{n\times k}$, $v\in\Bbb Z^n$ and variables $x_1,\dots,x_k$ given as a vector $x$ we know that solving $x\in\Bbb Z^k$ in $Ax\leq v$ is fixed parameter tractable. There is a deterministic algorithm that runs in $O((nk)^{ck})$ time for some $c>0$. What is the space complexity of the algorithm? Does it run in polynomial space?

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According to this answer, "the space complexity of the algorithm" is polynomial when ​ 2.5 < c .
That answer does not indicate the polynomial's exponent.

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  • $\begingroup$ Lenstra's alg is just dynamic programing memoization will make it poly space $\endgroup$ – T.... Mar 30 '17 at 17:41
  • $\begingroup$ I should not said memoization but said reusing same space $\endgroup$ – T.... Apr 1 '17 at 1:00

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