Constraint Satisfaction Problems

Outline

Constraint satisfaction problems (CSPs)

Example: Map-Coloring

Example: Map-Coloring

Constraint graph

Varieties of CSPs

Varieties of constraints

Example: Task Scheduling

Example: Cryptarithmetic

Real-world CSPs

Standard search formulation (incremental)

CSP Search tree size

Backtracking search

Backtracking search

Backtracking example

Backtracking example

Backtracking example

Backtracking example

Exercise - paint the town!

Constraint Graph

Improving backtracking efficiency

Most constrained variable

Most constraining variable

Least constraining value

Forward checking

Forward checking

Forward checking

Forward checking

Constraint propagation

Arc consistency

More on arc consistency

Arc consistency

Arc consistency

Arc Consistency Propagation

Arc consistency

Arc consistency algorithm AC-3

Time complexity of AC-3

Maintaining AC (MAC)

Special kinds of Consistency

All Different

K-consistency

Local search for CSPs

Example: 4-Queens

Summary

Midterm test

Homework #1

Checklist for HW #1