Approximation Ratio Calculator

---
name: approximation-ratio-calculator
description: Analyze and prove approximation ratios for optimization algorithms
allowed-tools:
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  - Read
  - Write
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metadata:
  specialization: computer-science
  domain: science
  category: complexity-theory
  phase: 6
graph:
  domains: [domain:computer-science]
  specializations: [specialization:theoretical-computer-science]
  skillAreas: [skill-area:np-hard-heuristics, skill-area:mathematical-reasoning, skill-area:dynamic-programming]
  workflows: [workflow:research-grant-lifecycle]
  roles: [role:computational-scientist, role:research-engineer]
---

# 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