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 ga…