# Fixed dimension Integer programming minus LLL in fixed parameter $NC$?

If you remove LLL part then is remaining part of

a. Lenstra algorithm

b. Barvinok algorithm

in $$O(f(n)(\log(mL))^c)$$ time on $$O(g(n)(mL)^c)$$ processors with fixed $$c>0$$ in fixed $$n$$ dimension, $$m$$ constraints and $$L$$ bit length input for some functions $$f,g:\Bbb R\rightarrow\Bbb R$$?

Note we know linear programming and convex programming are not in $$NC$$ in general dimension.

• I assume for your last comment you mean assuming $P \neq NC$? – Joshua Grochow Apr 1 '18 at 23:42
• @JoshuaGrochow yes that is correct. – 1.. Apr 2 '18 at 1:31