Independent domination of grids

Let i m , n denote the minimum size of an independent dominating set in the m -by- n grid. In this article a dynamic programming algorithm is described that computes i m , n for fixed m and arbitrary n . For m < 16 , the algorithm is used to determine i m , n as a function of n . For m , n ? 16 , it is proved that i m , n = ? ( m + 2 ) ( n + 2 ) / 5 ? - 4 by constructing corresponding independent dominating sets and by applying results on the minimum size of dominating sets. Thus the independent domination number is now known for all grids.