Agent-Skills.md

Agent Skills: Approximation Ratio Calculator

Analyze and prove approximation ratios for optimization algorithms

complexity-theoryID: a5c-ai/babysitter/approximation-ratio-calculator

Repository

a5c-ai/babysitter
a5c-aiLicense: MIT
244

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plugins/babysitter/skills/babysit/process/specializations/domains/science/computer-science/skills/approximation-ratio-calculator/SKILL.md

Skill Metadata

Name
approximation-ratio-calculator
Description
Analyze and prove approximation ratios for optimization algorithms

Approximation Ratio Calculator

Purpose

Provides expert guidance on analyzing approximation algorithms and proving approximation guarantees.

Capabilities

  • LP relaxation analysis
  • Integrality gap computation
  • Randomized rounding analysis
  • Approximation factor derivation
  • PTAS/FPTAS feasibility assessment
  • Inapproximability results analysis

Usage Guidelines

  1. Problem Setup: Formalize the optimization problem
  2. LP Relaxation: Construct and analyze LP relaxation
  3. Rounding Design: Design rounding scheme
  4. Ratio Proof: Prove approximation ratio
  5. Gap Analysis: Analyze integrality gap

Tools/Libraries

  • LP/ILP solvers
  • Symbolic computation
  • Proof assistants