A Linear Time Algorithm for the 3-neighbour Travelling Salesman Problem on Halin Graphs and Extensions
نویسنده
چکیده
The quadratic travelling salesman problem (QTSP) is to find a least cost Hamiltonian cycle in an edge-weighted graph. We define a restricted version of QTSP, the kneighbour 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. Further, these results are useful in establishing approximation bounds based on domination analysis. TSP(k) can be used to model various machine scheduling problems including an optimal routing problem for unmanned aerial vehicles (UAVs).
منابع مشابه
A Linear Time Algorithm for the $3$-Neighbour Traveling Salesman Problem on Halin graphs and extensions
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 al...
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