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role-algorithms:computational-complexity

Classify computational problems and design algorithms via complexity classes and reductions.

14|3|Updated Feb 22, 2026

Search Tags:#algorithm design #computational complexity #np-complete #approximation algorithms #parameterized complexity #reduction

Ready to run

npx skills add https://github.com/rnavarych/alpha-engineer --skill role-algorithms-computational-complexity

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: role-algorithms:computational-complexity
Source: https://github.com/rnavarych/alpha-engineer/tree/main/plugins/roles/role-algorithms/skills/computational-complexity
Command: npx skills add https://github.com/rnavarych/alpha-engineer --skill role-algorithms-computational-complexity

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes references (resource) components.

What problem does it solve?

This Skill helps in understanding and classifying the inherent difficulty of computational problems, guiding the choice between exact, approximation, or heuristic algorithmic approaches.

Core Features & Use Cases

Complexity Classification: Determine if a problem is in P, NP-complete, or NP-hard.
Reduction Proofs: Assist in proving a problem's NP-completeness by constructing polynomial-time reductions.
Algorithm Selection: Guide the selection of appropriate algorithms, including approximation schemes (PTAS, FPTAS), parameterized algorithms (FPT), and randomized or heuristic methods.
Use Case: Before embarking on a complex implementation, use this Skill to classify a new optimization problem as NP-hard, then leverage its guidance to select an FPTAS for a provable approximation guarantee.

Quick Start

Use the role-algorithms:computational-complexity skill to classify the hardness of the traveling salesman problem.

Frequently Asked Questions about role-algorithms:computational-complexity

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I prove a problem is NP-complete using polynomial-time reductions?▼

To prove NP-completeness, construct a polynomial-time reduction from a known NP-complete problem to your target problem. This Skill guides reduction proofs by structuring transformations and verifying complexity class membership.

What is the difference between PTAS and FPTAS approximation algorithms?▼

PTAS and FPTAS are approximation schemes for NP-hard problems, but FPTAS runs in fully polynomial time regarding input size and error margin. This Skill helps classify algorithmic paradigms to select schemes providing provable approximation guarantees.

How do I classify if my optimization problem is in P, NP-complete, or NP-hard?▼

Classify problem hardness by analyzing solution verifiability and reduction mappings to known complexity classes. This Skill evaluates whether your problem belongs to P, NP-complete, or NP-hard, guiding exact versus heuristic algorithm design choices.

When should I use parameterized complexity and FPT algorithms for intractable problems?▼

Use parameterized complexity and FPT algorithms when problem hardness is confined to a specific parameter, allowing fixed-parameter tractable solutions. This Skill identifies parameterized structures to design exact algorithms for otherwise intractable computational problems.

What is the best way to choose between randomized and heuristic approaches for NP-hard problems?▼

Choosing between randomized and heuristic approaches depends on required approximation bounds and runtime constraints. This Skill compares algorithmic paradigms for intractable problems, recommending randomized or heuristic methods when exact solutions are computationally infeasible.

Do I need to understand complexity classes before classifying problem hardness?▼

Understanding complexity classes is required, as this Skill relies on knowledge of P vs NP, NP-completeness, and reduction techniques to analyze computational complexity. It builds on these foundations to guide algorithmic paradigm selection.