CSP Solver

A high-performance Constraint Satisfaction Problem (CSP) solver library written in Rust.

We are starting the implementation from scratch.

Overview

This library provides efficient algorithms and data structures for solving constraint satisfaction problems. CSPs are mathematical problems defined as a set of objects whose state must satisfy a number of constraints or limitations.

Features

• Constraint Propagation: Advanced constraint propagation algorithms for domain reduction
• Backtracking Search: Efficient backtracking search with various heuristics
• Domain Management: Flexible domain representation and manipulation
• Multiple Constraint Types: Support for various constraint types (binary, n-ary, global)
• Search Strategies: Multiple search strategies and variable ordering heuristics
• High Performance: Optimized for speed with minimal memory allocation

Installation

Add this to your Cargo.toml:

[dependencies]
csp = "0.0.1"

Quick Start

use csp::*;

fn main() -> CspResult<()> {
    // Create a simple CSP
    let mut solver = CspSolver::new();
    
    // Add variables with domains
    let var1 = solver.add_variable("x", vec![1, 2, 3])?;
    let var2 = solver.add_variable("y", vec![1, 2, 3])?;
    
    // Add constraints
    solver.add_constraint(NotEqualConstraint::new(var1, var2))?;
    
    // Solve
    if let Some(solution) = solver.solve()? {
        println!("Solution found: {:?}", solution);
    } else {
        println!("No solution exists");
    }
    
    Ok(())
}

Examples

N-Queens Problem

use csp::*;

fn solve_n_queens(n: usize) -> CspResult<Option<Solution>> {
    let mut solver = CspSolver::new();
    
    // Create variables for each queen (column position in each row)
    let mut queens = Vec::new();
    for i in 0..n {
        let var = solver.add_variable(
            &format!("queen_{}", i), 
            (1..=n).collect()
        )?;
        queens.push(var);
    }
    
    // Add constraints: no two queens can attack each other
    for i in 0..n {
        for j in i + 1..n {
            // Different columns
            solver.add_constraint(NotEqualConstraint::new(queens[i], queens[j]))?;
            
            // Different diagonals
            solver.add_constraint(DiagonalConstraint::new(queens[i], queens[j], i, j))?;
        }
    }
    
    solver.solve()
}

Graph Coloring

use csp::*;

fn solve_graph_coloring(graph: &Graph, colors: usize) -> CspResult<Option<Solution>> {
    let mut solver = CspSolver::new();
    
    // Create variable for each node
    let mut nodes = Vec::new();
    for node in graph.nodes() {
        let var = solver.add_variable(
            &format!("node_{}", node.id()), 
            (1..=colors).collect()
        )?;
        nodes.push(var);
    }
    
    // Add constraints: adjacent nodes must have different colors
    for edge in graph.edges() {
        solver.add_constraint(NotEqualConstraint::new(
            nodes[edge.from()], 
            nodes[edge.to()]
        ))?;
    }
    
    solver.solve()
}

Architecture

The library is organized into several key modules:

• solver: Main CSP solver implementation
• variable: Variable representation and management
• domain: Domain operations and constraints
• constraints: Various constraint types and implementations
• propagation: Constraint propagation algorithms
• search: Search strategies and heuristics

Constraint Types

• Binary Constraints: Constraints between two variables
• N-ary Constraints: Constraints involving multiple variables
• Global Constraints: Specialized constraints for common patterns
• Custom Constraints: Support for user-defined constraints

Search Strategies

• Backtracking: Basic chronological backtracking
• Forward Checking: Backtracking with look-ahead
• MAC (Maintaining Arc Consistency): Advanced consistency checking
• Variable Ordering: Various heuristics (MRV, degree, etc.)
• Value Ordering: Least constraining value, etc.

Performance

The library is designed for high performance:

• Zero-cost abstractions where possible
• Efficient memory usage
• Optimized algorithms
• Benchmarks included in the repository

Contributing

Contributions are welcome! Please feel free to submit a Pull Request. For major changes, please open an issue first to discuss what you would like to change.

Development Setup

1. Clone the repository
2. Install Rust (latest stable version)
3. Run tests: cargo test
4. Run benchmarks: cargo bench

Code Style

This project follows standard Rust conventions:

• Use rustfmt for formatting
• Use clippy for linting
• Write documentation for public APIs
• Include tests for new functionality

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

• Inspired by classical CSP algorithms and research
• Built with performance and usability in mind
• Thanks to the Rust community for excellent tooling and libraries

Related Projects

• constraint - Another Rust CSP library
• satisfiability - SAT solver
• good_lp - Linear programming

References

• Artificial Intelligence: A Modern Approach (Russell & Norvig)
• Constraint Processing (Rina Dechter)
• Handbook of Constraint Programming (Rossi, van Beek, Walsh)

Status

The library is currently in active development. Features and APIs may change as we refine the implementation and add new functionality.