# Question

We mentioned iterative lengthening search, an iterative analog of uniform cost search. The idea is in use increasing limits on path cost. If a node is generated whose path cost exceeds the current limit, it is immediately discarded, for each new iteration the limit is set to the lowest path cost of any node discarded in the previous iteration.

a. Show that this algorithm is optimal for general path costs.

b. Consider a uniform tree with branching factor b, solution depth d. and unit step costs. How much iteration will iterative lengthening require?

c. Now consider step costs drawn from the continuous range [0. 1] with a minimum positive cost. How much iteration is required in the worst case?

d. Implement the algorithm and apply it to instances of the 8-puzzle and traveling salesperson problems. Compare the algorithm’s performance to that of uniform-cost search, and comment on your results.

a. Show that this algorithm is optimal for general path costs.

b. Consider a uniform tree with branching factor b, solution depth d. and unit step costs. How much iteration will iterative lengthening require?

c. Now consider step costs drawn from the continuous range [0. 1] with a minimum positive cost. How much iteration is required in the worst case?

d. Implement the algorithm and apply it to instances of the 8-puzzle and traveling salesperson problems. Compare the algorithm’s performance to that of uniform-cost search, and comment on your results.

## Answer to relevant Questions

Prove that uniform-cost search and breadth-first search with constant step costs are optimal when used with the GRAPH-SEARCH algorithm. Show a state space with constant step costs in which GRAPH-SEARCH using iterative ...Trace the operation of A* search applied to the problem of getting to Bucharest from Lugoj using the straight line distance heuristic. That is, show the sequence of nodes that the algorithm will consider and the f, y, and h ...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 ...Compare the performance of A and RBFS on a set of randomly generated problems in the 8-puzzle (with Manhattan distance) and TSP (with MST—see Exercise 4.8) domains. Discuss your results. What happens to the performance of ...AC-3 puts back on the queue every arc (Xk, Xi) whenever any value is deleted from the domain of Xi, even if each value of Xk is consistent with several remaining values of X. Suppose that, for every arc (Xk, Xi), we keep ...Post your question

0