Abstract
AnO(n log logn) (resp.O(n2 log2 n)) algorithm is presented to solve the minimum cardinality (resp. weight) dominating set problem on permutation graphs, assuming the input is a permutation. The best-known previous algorithm was given by FÄrber and Keil, where they use dynamic programming to get anO(n2 (resp.O(n3)) algorithm. Our improvement is based on the following three factors: (1) an observation on the order among the intermediate terms in the dynamic programming, (2) a new construction formula for the intermediate terms, and (3) efficient data structures for manipulating these terms.
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Communicated by Takao Asano.
This research was supported in part by the National Science Foundation under Grant CCR-8905415 to Northwestern University.
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Tsai, KH., Hsu, WL. Fast algorithms for the dominating set problem on permutation graphs. Algorithmica 9, 601–614 (1993). https://doi.org/10.1007/BF01190158
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DOI: https://doi.org/10.1007/BF01190158