1 research outputs found
Scalefree hardness of average-case Euclidean TSP approximation
We show that if PNP, then a wide class of TSP heuristics fail to
approximate the length of the TSP to asymptotic optimality, even for random
Euclidean instances. Previously, this result was not even known for any
heuristics (greedy, etc) used in practice. As an application, we show that when
using a heuristic from this class, a natural class of branch-and-bound
algorithms takes exponential time to find an optimal tour (again, even on a
random point-set), regardless of the particular branching strategy or
lower-bound algorithm used.Comment: 20 pages, 4 figure