Connected domination and dominating clique in trapezoid graphs

The class of trapezoid graphs is a subclass of cocomparability graphs and contains both the interval graphs and the permutation graphs. In this paper we present an O(n) time algorithm for the minimum cardinality connected dominating set problem and an O(n+m) time algorithm for the minimum cardinality dominating clique problem in trapezoid graphs. Both algorithms require the trapezoid diagram to be given as input.