# MCP Interface Implementation Plan
## Overview
This document outlines the plan to implement a Model Context Protocol (MCP) interface for the sublinear-time-solver project using the FastMCP TypeScript library. The MCP server will provide structured access to the solver algorithms and enable integration with AI assistants and other tools.
## Goals
1. Create an MCP server that exposes the sublinear-time solver functionality
2. Use FastMCP TypeScript library for rapid development
3. Distribute as an npx-executable package for easy installation
4. Provide both programmatic API and command-line interface
## Technology Stack
- **Language**: TypeScript
- **Framework**: FastMCP
- **Runtime**: Node.js
- **Package Manager**: npm/npx
- **Build Tool**: esbuild or tsx
- **Testing**: Jest or Vitest
## Project Structure
```
src/
├── mcp/
│ ├── server.ts # Main MCP server implementation
│ ├── tools/ # MCP tool definitions
│ │ ├── solver.ts # Solver-specific tools
│ │ ├── matrix.ts # Matrix operation tools
│ │ └── graph.ts # Graph algorithm tools
│ ├── resources/ # MCP resource providers
│ │ ├── algorithms.ts # Algorithm documentation resources
│ │ └── examples.ts # Example problems and solutions
│ ├── prompts/ # MCP prompt templates
│ │ └── solver.ts # Solver-specific prompts
│ └── index.ts # Entry point for MCP server
├── cli/
│ └── index.ts # CLI wrapper for npx execution
├── core/ # Core solver implementations
│ ├── types.ts # TypeScript type definitions
│ ├── matrix.ts # Matrix operations
│ ├── solver.ts # Main solver algorithms
│ └── utils.ts # Utility functions
└── tests/
├── mcp/ # MCP-specific tests
└── core/ # Core functionality tests
```
## Implementation Phases
### Phase 1: Core Setup (Week 1)
1. **Initialize TypeScript Project**
- Set up package.json with npx configuration
- Configure TypeScript with strict mode
- Install FastMCP and dependencies
- Set up build pipeline
2. **Define Core Types**
- Matrix representation types
- Solver configuration interfaces
- Result types with error handling
- MCP message types
3. **Basic MCP Server**
- Create minimal FastMCP server
- Implement health check endpoint
- Set up logging and error handling
- Test basic connectivity
### Phase 2: Solver Integration (Week 2)
1. **Implement Core Algorithms**
- Port existing solver algorithms to TypeScript
- Implement Neumann series expansion
- Add random walk sampling
- Implement forward/backward push methods
2. **Create MCP Tools**
```typescript
// Example tool definitions
- solveDiagonallyDominant: Solve ADD systems
- estimateCoordinate: Estimate single coordinate
- computePageRank: PageRank computation
- analyzeConvergence: Check convergence properties
```
3. **Add Resource Providers**
- Algorithm documentation
- Performance benchmarks
- Example matrices and solutions
- Configuration templates
### Phase 3: Advanced Features (Week 3)
1. **Bidirectional Solver**
- Implement forward-backward combination
- Add optimization heuristics
- Performance monitoring
2. **Streaming Support**
- Add streaming for large matrix operations
- Progress reporting for long-running computations
- Incremental result updates
3. **Caching Layer**
- Cache frequently accessed matrices
- Memoize intermediate computations
- Result caching with TTL
### Phase 4: CLI and Distribution (Week 4)
1. **CLI Implementation**
- Command-line argument parsing
- Interactive mode
- Output formatting (JSON, CSV, etc.)
- Progress indicators
2. **NPX Package Setup**
```json
{
"name": "sublinear-solver-mcp",
"bin": {
"sublinear-solver": "./dist/cli/index.js"
},
"scripts": {
"start": "node dist/mcp/index.js"
}
}
```
3. **Documentation**
- API documentation
- Usage examples
- Integration guides
- Performance tuning guide
## MCP Tool Specifications
### Core Tools
1. **solve**
```typescript
interface SolveParams {
matrix: number[][] | SparseMatrix;
vector: number[];
method?: 'neumann' | 'random-walk' | 'push';
epsilon?: number;
maxIterations?: number;
}
```
2. **estimateEntry**
```typescript
interface EstimateEntryParams {
matrix: number[][] | SparseMatrix;
row: number;
column: number;
epsilon: number;
confidence?: number;
}
```
3. **analyzeMatrix**
```typescript
interface AnalyzeMatrixParams {
matrix: number[][] | SparseMatrix;
checkDominance?: boolean;
computeGap?: boolean;
estimateCondition?: boolean;
}
```
### Graph Tools
1. **pageRank**
```typescript
interface PageRankParams {
adjacency: number[][] | SparseMatrix;
damping?: number;
personalized?: number[];
epsilon?: number;
}
```
2. **effectiveResistance**
```typescript
interface EffectiveResistanceParams {
laplacian: number[][] | SparseMatrix;
source: number;
target: number;
epsilon?: number;
}
```
## FastMCP Integration
### Server Configuration
```typescript
import { FastMCP } from '@fastmcp/core';
const server = new FastMCP({
name: 'sublinear-solver',
version: '1.0.0',
description: 'Sublinear-time solver for ADD systems'
});
// Register tools
server.tool('solve', solveTool);
server.tool('analyze', analyzeTool);
// Register resources
server.resource('algorithms/*', algorithmProvider);
server.resource('examples/*', exampleProvider);
// Register prompts
server.prompt('optimize', optimizationPrompt);
```
### Error Handling
```typescript
class SolverError extends Error {
constructor(
message: string,
public code: string,
public details?: any
) {
super(message);
}
}
// Error codes
const ErrorCodes = {
NOT_DIAGONALLY_DOMINANT: 'E001',
CONVERGENCE_FAILED: 'E002',
INVALID_MATRIX: 'E003',
TIMEOUT: 'E004'
};
```
## Performance Considerations
1. **Memory Management**
- Use sparse matrix representations
- Implement streaming for large datasets
- Clear caches periodically
2. **Computation Optimization**
- Use WebAssembly for critical paths
- Implement parallel processing where possible
- Adaptive algorithm selection based on matrix properties
3. **Network Efficiency**
- Compress large matrix transfers
- Use binary protocols for numerical data
- Implement request batching
## Testing Strategy
1. **Unit Tests**
- Core algorithm correctness
- Edge cases (singular matrices, etc.)
- Performance regression tests
2. **Integration Tests**
- MCP protocol compliance
- End-to-end solver workflows
- Error handling scenarios
3. **Performance Tests**
- Benchmark against reference implementations
- Scalability testing with large matrices
- Memory usage profiling
## Deployment
### NPX Distribution
```bash
# Users can run directly:
npx sublinear-solver-mcp serve
# Or install globally:
npm install -g sublinear-solver-mcp
sublinear-solver serve
```
### Docker Support
```dockerfile
FROM node:20-alpine
WORKDIR /app
COPY package*.json ./
RUN npm ci --only=production
COPY dist ./dist
EXPOSE 3000
CMD ["npm", "start"]
```
## Integration Examples
### With Claude Desktop
```json
{
"mcpServers": {
"sublinear-solver": {
"command": "npx",
"args": ["sublinear-solver-mcp", "serve"],
"env": {
"SOLVER_MAX_MEMORY": "2GB",
"SOLVER_TIMEOUT": "30000"
}
}
}
}
```
### Programmatic Usage
```typescript
import { SolverClient } from 'sublinear-solver-mcp';
const client = new SolverClient();
const result = await client.solve({
matrix: [[4, -1, 0], [-1, 4, -1], [0, -1, 4]],
vector: [1, 2, 1],
epsilon: 0.001
});
```
## Success Metrics
1. **Performance**
- Achieve sublinear time complexity for supported operations
- Handle matrices up to 1M×1M sparse entries
- Response time < 100ms for small matrices
2. **Reliability**
- 99.9% uptime for MCP server
- Graceful degradation for edge cases
- Comprehensive error messages
3. **Adoption**
- npm weekly downloads > 1000
- GitHub stars > 100
- Active community contributions
## Timeline
- **Week 1**: Core setup and basic MCP server
- **Week 2**: Algorithm implementation and tool creation
- **Week 3**: Advanced features and optimization
- **Week 4**: CLI, documentation, and release
- **Week 5**: Testing, bug fixes, and performance tuning
- **Week 6**: Release and community engagement
## Open Questions
1. Should we support GPU acceleration for large matrices?
2. What serialization format is optimal for sparse matrices?
3. Should we implement a web-based UI for visualization?
4. How to handle distributed computation for very large systems?
5. What telemetry/monitoring should be included?
## References
- [FastMCP Documentation](https://github.com/fastmcp/fastmcp)
- [MCP Specification](https://modelcontextprotocol.io)
- [Original Research Papers](../research.md)
- [TypeScript Best Practices](https://typescript.style)