Komponenta výukového serveru TI - NP-úplné problémy 1

Abstract

This bachelor thesis focuses on NP-complete problems and polynomial reductions, which form the foundation of computational complexity theory. The main goal is to make these concepts easier to understand through interactive visualization. The theoretical part defines the basic complexity classes and details nine polynomial reductions between classic problems (SAT, 3-SAT, 3-Coloring, Independent Set, Clique, and Vertex Cover). The practical output is a modern web application developed in TypeScript using the React library and the Next.js framework. The tool allows users to perform reductions between problems, observe the reduction process step-by-step, and subsequently find a solution for the resulting problem using optimized algorithms. To ensure a smooth user experience, computationally heavy tasks run in the background using a Web Worker. The application serves as a comprehensive educational tool for students and anyone interested in theoretical computer science.