Introduction

This repository implements the algorithm in the An 𝒪(3.82^k) Time FPT Algorithm for Convex Flip Distance, which was published in STACS 2023.

Building and Running

Please make sure you have cmake and a C++ compiler installed. We used Clang 11, but other compilers should work as well.

Clone or download this repository, and then go to the root directory of this project in the terminal. Run the following commands:

cmake -S . -B cmake-build-debug
cd cmake-build-debug
cmake --build .

The files generated by cmake will appear in the cmake-build-debug directory. You can run the following command to execute all unit tests.

cd cmake-build-debug
./Google_Tests_run

Project Structure

main.cpp and rand.cpp are entry points to the main program.

The triangulation folder contains classes for triangulations, binary trees, and binary strings. The TriangulatedGraph class stores triangulations and implements common operations such as flips. The BinaryTree class implements a basic binary tree, which is useful when the algorithm needs to convert a triangulation into a binary tree. BinaryString is a wrapper class for vector<bool> and facilitates conversions between different representations of a triangulation.

The algo folder contains 2 algorithms for computing flip distance: a simple breadth-first search algorithm and the FPT algorithm described in the STACS paper. The BFS algorithm is a baseline in performance tests and helps to verify the more complicated algorithm in the paper.

The tests folder contains some unit tests.

The utils folder contains a utility program that generates random triangulations.