The traveling salesperson problem (TSP) is difficult to solve for input instances with large number of cities. Instead of finding the solution of an input with a large number of cities, the problem is approximated into a simpler form containing smaller number of cities, which is then solved optimally. Graph pyramid solution strategies, in a bottom-up manner using Boruvka’s minimum spanning tree, convert a 2D Euclidean TSP problem with a large number of cities into successively smaller problems (graphs) with similar layout and solution, until the number of cities is small enough to seek the optimal solution. Expanding this tour solution in a top-down manner to the lower levels of the pyramid approximates the solution. The new model has an adaptive spatial structure and it simulates visual acuity and visual attention. The model solves the TSP problem sequentially, by moving attention from city to city with the same quality as humans. Graph pyramid data structures and processing strategies are a plausible model for finding near-optimal solutions for computationally hard pattern recognition problems.