Exercise 3.38

[tsp-mst-exercise]The traveling salesperson problem (TSP) can be solved with the minimum-spanning-tree (MST) heuristic, which estimates the cost of completing a tour, given that a partial tour has already been constructed. The MST cost of a set of cities is the smallest sum of the link costs of any tree that connects all the cities.

  1. Show how this heuristic can be derived from a relaxed version of the TSP.

  2. Show that the MST heuristic dominates straight-line distance.

  3. Write a problem generator for instances of the TSP where cities are represented by random points in the unit square.

  4. Find an efficient algorithm in the literature for constructing the MST, and use it with A graph search to solve instances of the TSP.

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