Trapezoid graphs and their coloring
Discrete Applied Mathematics
An O(n2) time algorithm for the 2-chain cover problem and related problems
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Dominations in trapezoid graphs
Information Processing Letters
Trapezoid graphs and generalizations, geometry and algorithms
Discrete Applied Mathematics
Weighted domination of cocomparability graphs
Discrete Applied Mathematics
Effincient Domination of Permutation Graphs and Trapezoid Graphs
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
Efficient Algorithms for the Minimum Connected Domination on Trapezoid Graphs
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
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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 [8], 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.