Description: Acknowledgement My most sincere thanks go to my adviser, Dr Maciej Slusarek, for his guidance, encouragement and support during the development of this work.
In our work we present two parallel algorithms and their lock-free implementations using a popular GPU environment Nvidia CUDA. The first algorithm is the push-relabel method for the flow problem in grid graphs. The second is the cost scaling algorithm for the assignment problem in complete bipartite graphs.