Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 15, Problem 4P
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Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a.
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There is an n × n grid of squares. Each square is either special, or has a positive integer costassigned to it. No square on the border of the grid is special.A set of squares S is said to be good if it does not contain any special squares and, starting fromany special square, you cannot reach a square on the border of the grid by performing up, down,left and right moves without entering a cell belonging to S.
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- Design an algorithm which receives an arbitrary n × n grid, runs in time poly-nomial in n and determines a good set of squares with minimum total cost.
Simulated annealing is an extension of hill climbing, which uses randomness to avoid getting stuck in local maxima and plateaux.
a) As defined in your textbook, simulated annealing returns the current state when the end of the annealing schedule is reached and if the annealing schedule is slow enough. Given that we know the value (measure of goodness) of each state we visit, is there anything smarter we could do?
(b) Simulated annealing requires a very small amount of memory, just enough to store two states: the current state and the proposed next state. Suppose we had enough memory to hold two million states. Propose a modification to simulated annealing that makes productive use of the additional memory.
In particular, suggest something that will likely perform better than just running simulated annealing a million times consecutively with random restarts. [Note: There are multiple correct answers here.]
(c) Gradient ascent search is prone to local optima just like hill climbing.…
Chapter 15 Solutions
Introduction to Algorithms
Ch. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.2 - Prob. 1ECh. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5E
Ch. 15.2 - Prob. 6ECh. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.4 - Prob. 1ECh. 15.4 - Prob. 2ECh. 15.4 - Prob. 3ECh. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.5 - Prob. 1ECh. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12P
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