Finding the minimum value of all subsets in a 2D array
In one dimension, looking for the maximum sum, this is solved by Kadane's algorithm. The referenced page does discuss some of the history and gives pointers to efficient solutions for the two-dimensional problem.
Bentley in his seventh &quot;Programming Pearls&quot; column (see e.g. here) discusses the one-dimensional problem in depth, devising ever more efficient algorithms for it's solution. Bentley's columns (and much more) are collected in his book &quot;Programming Pearls&quot; (Addison-Wesley, 2nd edition 1999).