Weighted independent perfect domination on cocomparability graphs Original Research Article

Suppose G = (V, E) is a graph in which every vertex v ϵ V is associated with a cost c(v). This paper studies the weighted independent perfect domination problem on G, i.e., the problem of finding a subset D of V such that every vertex in V is equal or adjacent to exactly one vertex in D and ∑c(v): v ϵ D is minimum. We give an O(¦V¦¦E¦) algorithm for the problem on cocomparability graphs. The algorithm can be implemented to run in O(¦V¦2.37) time. With some modifications, the algorithm yields an O(¦V¦+¦E¦) algorithm on interval graphs, which are special cocomparability graphs.