Pseudogeometric version of the traveling salesman problem: application in quantum physics models and a heuristic variant of point placement

The geometric version of the traveling salesman problem (TSP) has been extensively studied, leading to the development of various approaches for solving its special cases. However, these algorithms often fall short when applied to problems beyond the geometric TSP. In this paper, we explore the pseudo-geometric TSP version, a generalization of the geometric TSP, and propose an adapted geometric algorithm for solving its specific instances. We leverage the knowledge of error bounds to estimate the reconstruction error of the TSP solution even when using geometric approaches for the pseudogeometric TSP. This allows us to achieve reliable results despite uncertainties or noise in the data. We provide a concise description of our algorithmic adaptation and present the results of computational experiments to demonstrate its effectiveness.