We known $DET\in NC^2$.Supposing the given $n\times n$ matrix has at most $O(1)$ entries per row and column can we compute determinant in a class smaller than $NC^2$?can we compute determinant in $O(n)$ arithmetic operations?if each entry is in $\{0,\pm1\}$ can we compute determinant in $O(n)$ bit operations?
Complexity of very sparse determinant
cc.complexity theory;ds.algorithms;linear algebra;sparse matrix;determinant