Travelling salesman paths on Demidenko matrices
Eranda Cela (1), Vladimir G. Deineko (2), Gerhard J. Woeginger (3), ((1) Graz University of Technology, (2) Warwick business School, (3) RWTH, Aachen)

TL;DR
This paper identifies a new polynomially solvable case of the Path-TSP when the distance matrix is a Demidenko matrix, using combinatorial properties and a dynamic programming approach.
Contribution
It introduces a novel polynomial-time solution for Path-TSP on Demidenko matrices, expanding the class of efficiently solvable instances.
Findings
Polynomial-time algorithm for Path-TSP on Demidenko matrices
Key combinatorial properties of optimal solutions
Dynamic programming with O(n^6) complexity
Abstract
In the path version of the Travelling Salesman Problem (Path-TSP), a salesman is looking for the shortest Hamiltonian path through a set of n cities. The salesman has to start his journey at a given city s, visit every city exactly once, and finally end his trip at another given city t. In this paper we identify a new polynomially solvable case of the Path-TSP where the distance matrix of the cities is a so-called Demidenko matrix. We identify a number of crucial combinatorial properties of the optimal solution, and we design a dynamic program with time complexity .
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