Commonly we can find different choises in the application of Approximation algorithm. Three most used are:
Basic Distributed Greedy Vertex Cover Algorithm (adaptation of Parnas and Ron’s algorithm).
Distributed Vertex Cover via Greedy Matching Algorithm
Distributed Vertex Cover Algorithm with Breadth-First Search Tree
When we inspect the theoretical performances, we find out that the best one is the first algorithm.it has been observed the worst performance with the BFS tree based algorithm. The reason is that asynchronous BFS construction is a costly operation.