Independent domination of grids

Let im,nim,n denote the minimum size of an independent dominating set in the mm-by-nn grid. In this article a dynamic programming algorithm is described that computes im,nim,n for fixed mm and arbitrary nn. For m<16m<16, the algorithm is used to determine im,nim,n as a function of nn. For m,n≥16m,n≥16, it is proved that im,n=⌊(m+2)(n+2)/5⌋−4im,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.