Abstract
In this note, we give a proof that several vertex ordering problems can be solved in O ∗(2n) time and O ∗(2n) space, or in O ∗(4n) time and polynomial space. The algorithms generalize algorithms for the Travelling Salesman Problem by Held and Karp (J. Soc. Ind. Appl. Math. 10:196–210, 1962) and Gurevich and Shelah (SIAM J. Comput. 16:486–502, 1987). We survey a number of vertex ordering problems to which the results apply.
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This research was partially supported by the project Treewidth and Combinatorial Optimization with a grant from the Netherlands Organization for Scientific Research NWO and by the Research Council of Norway and by the DFG research group “Algorithms, Structure, Randomness” (Grant number GR 883/9-3, GR 883/9-4). The research of the last author was supported by the Spanish CICYT project TIN-2004-07925 (GRAMMARS). Parts of this paper appeared earlier in the conclusions section of [2].
D.M. Thilikos was supported by the project “Kapodistrias” (AΠ 02839/28.07.2008) of the National and Kapodistrian University of Athens (project code: 70/4/8757).
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Bodlaender, H.L., Fomin, F.V., Koster, A.M.C.A. et al. A Note on Exact Algorithms for Vertex Ordering Problems on Graphs. Theory Comput Syst 50, 420–432 (2012). https://doi.org/10.1007/s00224-011-9312-0
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DOI: https://doi.org/10.1007/s00224-011-9312-0