Loop topological complexity
Journal Title: Bulletin of Computational Applied Mathematics (Bull CompAMa) - Year 2015, Vol 3, Issue 2
Abstract
We introduce here the notion of loop motion planning algorithms and show that it yields to a homotopical invariant: the loop topological complexity, denoted throughout this paper by $\rm{TC}^{\rm{LP}}(-)$, which measures the algorithmic complexity of the motion of a drone as, for example, an unmanned airplane or a guided TV camera. Our main result states that $\rm{TC}(-) = \rm{TC}^{\rm{LP}}(-)$, where $\rm{TC}$ denotes the ordinary topological complexity introduced by M. Farber. Some interesting applications will emerge and will be discussed.
Authors and Affiliations
Younes Derfoufi, My Ismail Mamouni
Keywords
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