Overview
Constraint satisfaction backtracking tries candidate values, checks constraints early, and backtracks when a partial assignment cannot lead to a solution.
CoreSource checked
Constraint Satisfaction Backtracking
Solves constraint problems by assigning variables recursively and undoing inconsistent choices.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Optimization
- Difficulty
- Intermediate
- Family
- Constraint Search
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
partial assignmentconstraint propagationbacktrackingsearch pruning
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(1)
Average
O(d^n)
Worst
O(d^n)
Space
O(n)
When to Use
- Use when tuning model parameters needs partial assignment.
- Use when the input matches the assumptions behind constraint Search.
When Not to Use
- Avoid when the objective is cheap and convex enough for a simpler exact solver.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Solves constraint problems by assigning variables recursively and undoing inconsistent choices
- Uses partial assignment and constraint propagation to guide the work.
- Produces best candidate.
Use Cases
- Tuning model parameters
- Searching design spaces
- Fitting models to noisy data
Inputs
- Objective function
- Initial candidate or population
- Stopping rule
Outputs
- Best candidate
- Objective value
- Search history
Key Formulas (1)
Consistency test
valid(partialassignment, constraints) = true
valid(partial_assignment, constraints) = trueAllows recursion to continue only when all checked constraints are satisfied.
Pseudocode
- 1.Prepare the inputs and state needed for Constraint Satisfaction Backtracking.
- 2.Apply the partial assignment step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return best candidate.
Canonical Example
- Input
- Constraint Satisfaction Backtracking input with a small representative case
- Output
- Best candidate
- Explanation
- Constraint Satisfaction Backtracking applies partial assignment to produce best candidate.
Implementation Notes
- Track both best-so-far and current candidate state.
- Keep the partial assignment step separate enough to test independently.
Common Pitfalls
- Stopping too early can make a poor local result look like convergence.
- Forgetting to check edge cases can make Constraint Satisfaction Backtracking look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryPlot candidate points, objective values, and improvement steps across iterations.
Step 1 of 4: Prepare the inputs and state needed for Constraint Satisfaction Backtracking.
optimization-mechanismNotes
Constraint Satisfaction Backtracking should be used with the assumptions and tradeoffs of constraint Search in mind.
Sources (1)
What each reference supports for this entry.
Artificial Intelligence: A Modern Approach
BookReference text for search, local search, beam search, and constraint-satisfaction backtracking.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
UsesDepth-First Search
Graph Traversal · Foundation
Backtracking typically explores assignments through depth-first recursive search.
Compare with thisRelationships
View full relationship pageConceptual neighborBranch and Bound
Both prune a search tree using constraints or bounds.
Backtracking typically explores assignments through depth-first recursive search.
Related Algorithms
Tags
OptimizationConstraint SolvingBacktrackingSearch