Abstract
The weighted independent domination problem in trapezoid graphs was solved in O(n2) time [1]; the weighted efficient domination problem in trapezoid graphs was solved in O(n log log n + m) time , where ¯m denotes the number of edges in the complement of the trapezoid graph. In this paper, we show that the minimum weighted independent dominating set and the minimum weighted efficient dominating set in trapezoid graphs can both be found in O(n log n) time. Both of the algorithms require only O(n) space. Since ¯m can be as large as Ω(n2), comparing to previous results, our algorithms clearly give more efficient solutions to the related problems.
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