# Question: The traveling salesperson problem TSP can be solved via the

The traveling salesperson problem (TSP) can be solved via the minimum spanning tree (MST) heuristic, which is used to estimate 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.

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

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

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

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

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

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

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

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

**View Solution:**## Answer to relevant Questions

We defined the relaxation of the 8-puzzle in which a tile can move from square A to square B if B is blank. The exact solution of this problem defines Gaschnig’s heuristic (Gaschnig, 1979). Explain why Gaschnig’s ...In this exercise, we will explore the use of local search methods to solve TSPs of the type defined in Exercise 4.8.a. Devise a hill-climbing approach to solve TSPs. Compare the results with optimal solutions obtained via ...Give precise formulations for each of the following as constraint satisfaction problems:a. Rectilinear floor-planning: find non-overlapping places in a large rectangle for a number of smaller rectangles.b. Class scheduling: ...This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s Similarly, On is ...The Chinook checkers program makes extensive use of endgame databases, which provide exact values for every position with eight or fewer pieces. How might such databases be generated efficiently?Post your question