Quasiabelian landscapes of the traveling salesman problem are elementary

Authors:
Andrew Solomon;Bruce W. Colletti
Affiliations:
University of Technology, Sydney, P.O. Box 123 Broadway, NSW 2007, Australia;Florida Institute of Technology University College, National Capital Region Graduate Center, 4875 Eisenhower Ave, Suite 200, Alexandria VA 22304.7330, USA
Venue:
Discrete Optimization
Year:
2009

Citing 2
Cited 0

On quasiabelian Cayley graphs and graphical doubly regular representations

Discrete Mathematics - Algebraic and topological methods in graph theory
Local search and the local structure of NP-complete problems

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

Regarding a permutation as a (multi-traveler) tour of the traveling salesman problem, we show that-regardless of the distance matrix-the landscape based on a quasiabelian Cayley graph belongs to the class of elementary landscapes, where the cost vector is an eigenvector of the Cayley Laplacian, and where local minima are below average. The quasiabelian case has the additional property that, because the cost vector is an eigenvector of the Cayley Laplacian, the landscape can be reduced into independent components under a Fourier transformation. We indicate the way this may result in parallel (and therefore computationally distributed) traversal of the landscape.