Quiz Feb. 02 2006

Inf. Search & CSP

ca

d

e

b

SEARCH TREE

CONSTRAINT GRAPH

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(BG2) = 9, h(DG2)=10, h(AG1)=2, h(CG1)=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.

G1 G2

C D

A B

R1

2

10

9

1

1

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 followingheuristics: minimum value heuristic, degree heuristic, forward checking. Explain each step of your answer.

ca

d

e

b

SEARCH TREE

CONSTRAINT GRAPH

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(BG2) = 9, h(DG2)=10, h(AG1)=2, h(CG1)=1

a) [5pts] BACG1

f-value:1+99+210+111 G1 G2

C D

A B

R1

2

10

9

1

1

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=2FC+MVH+DH c=3FC+MVH d=4FC e=1