A Note on Exact Algorithms for Vertex Ordering Problems on Graphs

Authors:
Hans L. Bodlaender;Fedor V. Fomin;Arie M. C. A. Koster;Dieter Kratsch;Dimitrios M. Thilikos
Affiliations:
Utrecht University, Department of Information and Computing Sciences, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands;University of Bergen, Department of Informatics, 5020, Bergen, Norway;RWTH Aachen University, Lehrstuhl II für Mathematik, Wüllnerstr. 5b, 52062, Aachen, Germany;Université de Metz, LITA, 507045, Metz Cedex 01, France;National and Kapodistrian University of Athens, Department of Mathematics, Panepistimioupolis, 15784, Athens, Greece
Venue:
Theory of Computing Systems
Year:
2012

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Abstract

In this note, we give a proof that several vertex ordering problems can be solved in O ∗(2 n ) time and O ∗(2 n ) space, or in O ∗(4 n ) 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.