A Linear Time Algorithm for the 3-neighbour Traveling Salesman Problem
on Halin graphs and extensions
release_sgki4xxk45fp7jhegekflsiuhe
by
Brad Woods, Abraham Punnen, Tamon Stephen
2017
Abstract
The Quadratic Travelling Salesman Problem (QTSP) is to find a least cost
Hamilton cycle in an edge-weighted graph, where costs are defined on all pairs
of edges contained in the Hamilton cycle. This is a more general version than
the commonly studied QTSP which only considers pairs of adjacent edges. We
define a restricted version of QTSP, the k-neighbour TSP (TSP(k)), and give
a linear time algorithm to solve TSP(k) on a Halin graph for k≤ 3. This
algorithm can be extended to solve TSP(k) on any fully reducible class of
graphs for any fixed k in polynomial time. This result generalizes
corresponding results for the standard TSP. TSP(k) can be used to model
various machine scheduling problems as well as an optimal routing problem for
unmanned aerial vehicles (UAVs).
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