Finding a minimum independent dominating set in a permutation graph

Abstract We give a linear time reduction of the problem of finding a minimum independent dominating set in a permutation graph, into that of finding a shortest maximal increasing subsequence. We then give an O( n log 2 n )-time algorithm for solving the second (and hence the first) problem. This improves on the O ( n 3 )-time algorithm given in [4] for solving the problem of finding a minimum independent dominating set in a permutation graph.