The Dominating Set Problem on Shiftable Interval Graphs

In this paper the problem of computing a minimum dominating set of a Shiftable Interval Graph (SIG) is studied. SIG's can be considered a generalization of interval graphs, in the sense that a SIG identifies a whole family of interval graphs. An optimization problem defined on a SIG consists in determining an interval graph of the family which optimizes the value of the chosen measure. In this paper, in particular, we studied the problem of minimizing the cardinality d(S) of a dominating set. The problem is formally stated, its strong NP-completeness is proved, and upper and lower bounds for d(S) are discussed. Special cases solvable at optimality are characterized. Several algorithms are proposed to solve the problem on arbitrary SIG's, and are tested on 220 randomly chosen problem and on five ad hoc designed examples which emphasize the differences among the proposed algorithms.