approximation-ratio-calculator

name	approximation-ratio-calculator
description	Analyze and prove approximation ratios for optimization algorithms
allowed-tools	["Bash","Read","Write","Edit","Glob","Grep"]
metadata	{"specialization":"computer-science","domain":"science","category":"complexity-theory","phase":6}
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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