chapter5 - Constraint Satisfaction Problems CHAPTER 5...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
CHAPTER 5 HASSAN KHOSRAVI SPRING2011 Constraint Satisfaction Problems
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Outline CSP examples Backtracking search for CSPs Problem structure and problem decomposition Local search for CSPs
Background image of page 2
Constraint satisfaction problems (CSPs) CSP: state is defined by variables X i with values from domain D i goal test is a set of constraints specifying allowable combinations of values for subsets of variables Allows useful general-purpose algorithms with more power than standard search algorithms
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example: Map-Coloring
Background image of page 4
CSPs (continued) An assignment is complete when every variable is mentioned. A solution to a CSP is a complete assignment that satisfies all constraints. Some CSPs require a solution that maximizes an objective function . Examples of Applications: Airline schedules Cryptography Computer vision -> image interpretation Scheduling your MS or PhD thesis exam
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example: Map-Coloring contd.
Background image of page 6
Constraint graph Binary CSP: each constraint relates at most two variables Constraint graph: nodes are variables, arcs show constraints General-purpose CSP algorithms use the graph structure to speed up search. E.g., Tasmania is an independent subproblem!
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Varieties of constraints Unary constraints involve a single variable, e.g., SA 6= green Binary constraints involve pairs of variables, e.g., SA <> WA Higher-order constraints involve 3 or more variables Preferences (soft constraints), e.g., red is better than green often representable by a cost for each variable assignment constrained optimization problems
Background image of page 8
c a d e b 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. Problem
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example: 4-Queens Problem 1 3 2 4 3 2 4 1 X1 { 1 ,2,3,4} X3 {1,2,3,4} X4 {1,2,3,4} X2 {1,2,3,4}
Background image of page 10
Standard search formulation (incremental) Let’s start with the straightforward, dumb approach, then fix it States are defined by the values assigned so far Initial state: the empty assignment, { } Successor function: assign a value to an unassigned variablethat does not conflict with current assignment. fail if no legal assignments (not fixable!) Goal test: the current assignment is complete This is the same for all CSPs!
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Standard search formulation (incremental) Can we use breadth first search? Branching factor at top level? nd any of the d values can be assigned to any variable Next level? (n-1)d
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 67

chapter5 - Constraint Satisfaction Problems CHAPTER 5...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online