Quiz Feb. 02 2006 Inf. Search & CSP

G1 G2 C D A B R 1 2 10 9 1) Consider the search tree to the right. There are 2 goal states, G1 and G2. The numbers on the edges represent step-costs. You also know the following heuristic estimates: h(BG2) = 9, h(DG2)=10, h(AG1)=2, h(CG1)=1 a) [5pts] In what order will A* search visit the nodes? Explain your answer by indicating the value of the evaluation function for those nodes that the algorithm considers. SEARCH TREE 2) Consider the constraint graph on the right. The domain for every variable is [1,2,3,4]. There are 2 unary constraints: - variable “a” cannot take values 3 and 4. - variable “b” cannot take value 4. There are 8 binary constraints stating that variables connected by an edge cannot have the same value. a) [5pts] Find a solution for this CSP by using the following heuristics: minimum value heuristic, degree heuristic, forward checking. Explain each step of your answer. c a d e b CONSTRAINT GRAPH

G1 G2 C D A B R 1 2 10 9 1) Consider the search tree to the right. There are 2 goal states, G1 and G2. The numbers on the edges represent step-costs. You also know the following heuristic estimates: h(BG2) = 9, h(DG2)=10, h(AG1)=2, h(CG1)=1 a) [5pts] BACG1 f-value:1+99+210+111 SEARCH TREE 2) Consider the constraint graph on the right. The domain for every variable is [1,2,3,4]. There are 2 unary constraints: - variable “a” cannot take values 3 and 4. - variable “b” cannot take value 4. There are 8 binary constraints stating that variables connected by an edge cannot have the same value. a) [5pts] MVH a=1 (for example) FC+MVH b=2 FC+MVH+DH c=3 FC+MVH d=4 FC e=1 c a d e b CONSTRAINT GRAPH