ICS 171Fall 2005Homework #3(Due Th. Oct.20)1) Exercise 5.2 (pg 158)2) Exercise 5.3 (pg 158)3) Exercise 5.5 (pg 159)4) Consider the following binary constraint network: There are 4 variables: X1, X2, X3, X4 with the domains: D1={1,2,3,4}, D2={3,4,5,8,9},D3={2,3,5,6,7,9}, D4={3,5,7,8,9}. The constraints are X1≥X2, X2>X3 or X3-X2=2, X3≠X4.a. Write the constraints in a relational form and draw the constraint graph.b. Is the network arc-consistent? If not, compute the arc-consistent network. (show the whole process of enforcing arc-consistency and not just the finalnetwork)c. Is the network consistent? If yes, give a solution.5) Consider the 8 squares positioned as follows:The task is to label the boxes above with the numbers 1-8 such that the labels of any pair of adjacent squares (i.e. horizontal, vertical or diagonal) differ by at least 2 (i.e. 2 or more).a. Write the constraint graph in a relational form and draw the constraint graph.ICS 171Fall 2005b. Is the network arc-consistent? If not, compute the arc-consistent network. (show the whole process of enforcing arc-consistency and not just the finalarc-consistent network)c. Is the network consistent? If yes, give a solution. 6) Use the min-conflict (local search) method to solve the 4-Queen problem. Start with the queens on the main diagonal. Break ties
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