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Also known as: CSP
Finding assignments satisfying constraints across variables.
DESCRIPTION
A CSP specifies variables, domains, and constraints, seeking a consistent assignment. Solving uses backtracking, constraint propagation (arc consistency), and heuristics like MRV and least constraining value. CSPs model scheduling, timetables, puzzles, and configuration. They underpin SAT/SMT solving and constraint programming systems. Performance hinges on propagation and smart variable/value ordering.
ALTERNATIVE DEFINITIONS
UC Berkeley
A constraint satisfaction problem consists of variables with domains and constraints; the goal is to assign values to variables that satisfy all constraints.
Clarifies structure and objective of CSPs.
Stanford University
CSPs are defined by a set of variables, each with a domain, and a set of constraints limiting allowable combinations of values.
Emphasizes variables, domains, and constraint relations.
RELATED TERMS
Constraint Programming Backtracking Arc Consistency Forward Checking SAT Solver Search Domain Pruning Graph Coloring Sudoku SMT Solver
COMPETING TERMS
Optimization Problem Mixed-Integer Programming
KNOWLEDGE AREAS
AI Mathematics Semantic & Knowledge Modeling Data Science
TARGET AUDIENCE
AI Engineer Data Scientist Software Developer
EXTERNAL SOURCES
- Wikipedia - Constraint satisfaction problem
- MiniZinc - Constraint modeling language and tools
- Google OR-Tools - CP-SAT solver documentation
- IBM ILOG CP Optimizer - Constraint programming docs
TOP QUESTIONS
What is a Constraint Satisfaction Problem?
It’s a model with variables, domains, and constraints seeking assignments that satisfy all constraints. Solutions may be found via search and propagation.
Category: Definition
Which heuristics help solve CSPs efficiently?
MRV, degree heuristic, and least constraining value improve variable and value ordering. Good heuristics speed up backtracking.
Category: Requirements
How does arc consistency work in CSPs?
Arc consistency prunes domain values that lack support, reducing search space before or during backtracking.
Category: Example
What are common mistakes when modeling CSPs?
Overly tight constraints cause unsatisfiability; vague constraints yield too many solutions. Mis-specified domains derail performance.
Category: Mistakes
How do CSPs relate to SAT?
CSPs can be reduced to SAT; SAT solvers exploit powerful propagation and learning to solve such formulations.
Category: Topic
What risks arise in CSP solution strategies?
Poor heuristics or missing propagation lead to exponential blowups. Model errors cause infeasible searches.
Category: Risks
Where are CSPs applied in practice?
Scheduling, timetabling, resource allocation, circuit design, and puzzle solving are classic CSP applications.
Category: Overview
Are CSPs only academic?
No. Industrial solvers tackle real scheduling and configuration tasks with significant operational impact.
Category: Misunderstanding
What’s the difference between CSP and optimization?
CSP seeks feasibility; optimization seeks the best feasible solution under an objective.
Category: Alternatives