Traveling Salesperson Problem

This is an example of the classic traveling salesperson problem.

Formally, we are given a set of n nodes V (points, vertices, cities, holes), and a distance function tex2html_wrap_inline124 giving travel time between any given pair of nodes.

We want to find a tour (Hamiltonian circuit, permutation) of the nodes tex2html_wrap_inline126 such that tex2html_wrap_inline128 is minimized. It's the shortest trip that visits every city once and only once.

We'll assume the distance function D is symmetric: D(u,v)=D(v,u) for all u and v in V.

In the metric TSP, we additionally assume that distances obey the triangle inequality: for all u and v and w in V, tex2html_wrap_inline148 (shortcut is never worse).


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