Advertisement

Milling a Graph with Turn Costs: A Parameterized Complexity Perspective

  • Mike Fellows
  • Panos Giannopoulos
  • Christian Knauer
  • Christophe Paul
  • Frances Rosamond
  • Sue Whitesides
  • Nathan Yu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)

Abstract

The Discrete Milling problem is a natural and quite general graph-theoretic model for geometric milling problems: Given a graph, one asks for a walk that covers all its vertices with a minimum number of turns, as specified in the graph model by a 0/1 turncost function f x at each vertex x giving, for each ordered pair of edges (e,f) incident at x, the turn cost at x of a walk that enters the vertex on edge e and departs on edge f. We describe an initial study of the parameterized complexity of the problem.

Keywords

Grid Graph Directed Walk Free Pair Monochromatic Path Decomposable Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arkin, E., Bender, M., Demaine, E., Fekete, S., Mitchell, J., Sethia, S.: Optimal covering tours with turn costs. SIAM J. Computing 35(3), 531–566 (2005)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Dorn, F., Penninkx, E., Bodlaender, H., Fomin, F.: Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 95–106. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  4. 4.
    Fellows, M., Fomin, F., Lokshtanov, D., Rosamond, F., Saurabh, S., Szeider, S., Thomassen, C.: On the complexity of some colorful problems parameterized by treewidth. In: Dress, A.W.M., Xu, Y., Zhu, B. (eds.) COCOA. LNCS, vol. 4616, pp. 366–377. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)MATHGoogle Scholar
  6. 6.
    Held, M.: On the Computational Geometry of Pocket Machining. LNCS, vol. 500. Springer, Heidelberg (1991)MATHGoogle Scholar
  7. 7.
    Niedermeier, R.: Invitation to Fixed Parameter Algorithms, vol. 31. Oxford University Press, Oxford (2006)CrossRefMATHGoogle Scholar
  8. 8.
    Szeider, S.: Not so easy problems for tree decomposable graphs. In: International Conference on Discrete Mathematics (ICDM), pp. 161–171 (2008) (invited talk)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mike Fellows
    • 1
  • Panos Giannopoulos
    • 2
  • Christian Knauer
    • 3
  • Christophe Paul
    • 4
  • Frances Rosamond
    • 1
  • Sue Whitesides
    • 5
  • Nathan Yu
  1. 1.PCRU, Office of DVC(Research)University of NewcastleAustralia
  2. 2.Institut für InformatikFreie Universität BerlinBerlinGermany
  3. 3.Institut für InformatikUniversität BayreuthBayreuthGermany
  4. 4.NRS - LIRMMMontpellierFrance
  5. 5.Department of Computer ScienceUniversity of VictoriaCanada

Personalised recommendations