### Inhalt des Dokuments

## Flip Distance is in FPT time O(n+ k * c^k)

**Prof.
****Iyad Kanj (****DePaul
University**)

Let T be a triangulation of a set P of n points in the plane, and
let e be an edge shared by two triangles in T such that the
quadrilateral Q formed by these two triangles is convex. A flip of e
is the operation of replacing e by the other diagonal of Q to obtain a
new triangulation of P from T. The flip distance between two
triangulations of P is the minimum number of flips needed to transform
one triangulation into the other. The Flip Distance problem asks if
the flip distance between two given triangulations of P is k, for some
given k in N. It is a fundamental and a challenging problem whose
complexity for the case of triangulations of a convex polygon remains
open for over 25 years.

In this talk we present an
algorithm for the Flip Distance problem that runs in time O(n + k *
c^k), for a constant c <= 2 * 14^11, which implies that the problem
is fixed-parameter tractable. The NP-hardness reduction for the Flip
Distance problem given by Lubiw and Pathak can be used to show that,
unless the exponential-time hypothesis (ETH) fails, the Flip Distance
problem cannot be solved in time O*(2^{o(k)}). Therefore, one cannot
expect an asymptotic improvement in the exponent of the running time
of our algorithm.

Date | Speaker | Location | Language |
---|---|---|---|

23.10.2014 16:15 | Iyad
Kanj | TEL
512 | english |

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