Teaching dynamic programming techniques using permutation graphs
SIGCSE '95 Proceedings of the twenty-sixth SIGCSE technical symposium on Computer science education
An optimal algorithm for finding biconnected components in permutation graphs
CSC '95 Proceedings of the 1995 ACM 23rd annual conference on Computer science
An Optimal Algorithm for Finding the Minimum Cardinality Dominating Set on Permutation Graphs
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Graph classes with structured neighborhoods and algorithmic applications
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
An O(n)-time algorithm for the paired domination problem on permutation graphs
European Journal of Combinatorics
Graph classes with structured neighborhoods and algorithmic applications
Theoretical Computer Science
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Farber and Keil [ Algorithmica, 4 (1989), pp. 221--236] presented an $O(n^3)$-time algorithm for finding a minimum-weight dominating set in permutation graphs. This result was improved to $O(n^2 \log^2n)$ by Tsai and Hsu [SIGAL '90 Algorithms, Lecture Notes in Computer Science, Springer-Verlag, New York, 1990, pp. 109--117] and to $O(n(n + m))$ by the authors of this paper [ Inform. Process. Lett., 37 (1991), pp. 219--224], respectively. In this paper, we introduce a new faster algorithm that takes only $O(n + m)$ time to solve the same problem, where $m$ is the number of edges in a graph of $n$ vertices.