Boundary-Optimal triangulation flooding

  • Authors:
  • Richard J. Nowakowski;Norbert Zeh

  • Affiliations:
  • Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada;Faculty of Computer Science, Dalhousie University, Halifax, NS, Canada

  • Venue:
  • ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
  • Year:
  • 2004

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Abstract

Given a planar triangulation all of whose faces are initially white, we study the problem of colouring the faces black one by one so that the boundary between black and white faces as well as the number of connected black and white regions are small at all times We call such a colouring sequence of the triangles a flooding Our main result shows that it is in general impossible to guarantee boundary size ${\mathcal O}(n^{1-\epsilon})$, for any ε0, and a number of regions that is o(log n), where n is the number of faces of the triangulation We also show that a flooding with boundary size ${\mathcal O}(\sqrt{n})$ and ${\mathcal O}({\rm log}n)$ regions can be computed in ${\mathcal O}({\it n} {\rm log}n)$ time.