Given an n by m matrix of integers, there is a well known problem of finding the submatrix with maximum sum. This can be solved with a 2d version of Kadane's algorithm. An explanation of an O(nm^2) time algorithm for the 2D version which is based on Kadane's algorithm can be found here.
I am interested in a simpler version where only submatrices that include the top left cell of the matrix are considered. Can this version be solved faster in O(nm) time? If so, how can you do it? I would also like to see what the optimal submatrix is, not just its sum.