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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

Create an MCP server that exposes the sublinear-time solver functionality
Use FastMCP TypeScript library for rapid development
Distribute as an npx-executable package for easy installation
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)

Initialize TypeScript Project
- Set up package.json with npx configuration
- Configure TypeScript with strict mode
- Install FastMCP and dependencies
- Set up build pipeline
Define Core Types
- Matrix representation types
- Solver configuration interfaces
- Result types with error handling
- MCP message types
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)

Implement Core Algorithms
- Port existing solver algorithms to TypeScript
- Implement Neumann series expansion
- Add random walk sampling
- Implement forward/backward push methods

Create MCP Tools

// Example tool definitions
- solveDiagonallyDominant: Solve ADD systems
- estimateCoordinate: Estimate single coordinate
- computePageRank: PageRank computation
- analyzeConvergence: Check convergence properties

Add Resource Providers
- Algorithm documentation
- Performance benchmarks
- Example matrices and solutions
- Configuration templates

Phase 3: Advanced Features (Week 3)

Bidirectional Solver
- Implement forward-backward combination
- Add optimization heuristics
- Performance monitoring
Streaming Support
- Add streaming for large matrix operations
- Progress reporting for long-running computations
- Incremental result updates
Caching Layer
- Cache frequently accessed matrices
- Memoize intermediate computations
- Result caching with TTL

Phase 4: CLI and Distribution (Week 4)

CLI Implementation
- Command-line argument parsing
- Interactive mode
- Output formatting (JSON, CSV, etc.)
- Progress indicators

NPX Package Setup

{
  "name": "sublinear-solver-mcp",
  "bin": {
    "sublinear-solver": "./dist/cli/index.js"
  },
  "scripts": {
    "start": "node dist/mcp/index.js"
  }
}

Documentation
- API documentation
- Usage examples
- Integration guides
- Performance tuning guide

MCP Tool Specifications

Core Tools

solve

interface SolveParams {
  matrix: number[][] | SparseMatrix;
  vector: number[];
  method?: 'neumann' | 'random-walk' | 'push';
  epsilon?: number;
  maxIterations?: number;
}

estimateEntry

interface EstimateEntryParams {
  matrix: number[][] | SparseMatrix;
  row: number;
  column: number;
  epsilon: number;
  confidence?: number;
}

analyzeMatrix

interface AnalyzeMatrixParams {
  matrix: number[][] | SparseMatrix;
  checkDominance?: boolean;
  computeGap?: boolean;
  estimateCondition?: boolean;
}

Graph Tools

pageRank

interface PageRankParams {
  adjacency: number[][] | SparseMatrix;
  damping?: number;
  personalized?: number[];
  epsilon?: number;
}

effectiveResistance

interface EffectiveResistanceParams {
  laplacian: number[][] | SparseMatrix;
  source: number;
  target: number;
  epsilon?: number;
}

FastMCP Integration

Server Configuration

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

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

Memory Management
- Use sparse matrix representations
- Implement streaming for large datasets
- Clear caches periodically
Computation Optimization
- Use WebAssembly for critical paths
- Implement parallel processing where possible
- Adaptive algorithm selection based on matrix properties
Network Efficiency
- Compress large matrix transfers
- Use binary protocols for numerical data
- Implement request batching

Testing Strategy

Unit Tests
- Core algorithm correctness
- Edge cases (singular matrices, etc.)
- Performance regression tests
Integration Tests
- MCP protocol compliance
- End-to-end solver workflows
- Error handling scenarios
Performance Tests
- Benchmark against reference implementations
- Scalability testing with large matrices
- Memory usage profiling

Deployment

NPX Distribution

# Users can run directly:
npx sublinear-solver-mcp serve

# Or install globally:
npm install -g sublinear-solver-mcp
sublinear-solver serve

Docker Support

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

{
  "mcpServers": {
    "sublinear-solver": {
      "command": "npx",
      "args": ["sublinear-solver-mcp", "serve"],
      "env": {
        "SOLVER_MAX_MEMORY": "2GB",
        "SOLVER_TIMEOUT": "30000"
      }
    }
  }
}

Programmatic Usage

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

Performance
- Achieve sublinear time complexity for supported operations
- Handle matrices up to 1M×1M sparse entries
- Response time < 100ms for small matrices
Reliability
- 99.9% uptime for MCP server
- Graceful degradation for edge cases
- Comprehensive error messages
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

Should we support GPU acceleration for large matrices?
What serialization format is optimal for sparse matrices?
Should we implement a web-based UI for visualization?
How to handle distributed computation for very large systems?
What telemetry/monitoring should be included?

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