A linear time algorithm to compute a maximum weighted independent set on cocomparability graphs

Abstract The maximum weight independent set (WMIS) problem is a well-known NP-hard problem. It is a generalization of the maximum cardinality independent set problem where all the vertices have identical weights. There is an O ( n 2 ) time algorithm to compute a WMIS for cocomparability graphs by computing a maximum weight clique on the corresponding complement of the graph [1] . We present the first O ( m + n ) time algorithm to compute a WMIS directly on the given cocomparability graph, where m and n are the number of edges and vertices of the graph respectively. As a corollary, we get the minimum weight vertex cover of a cocomparability graph in linear time as well.