Another way to describe your greedy solution for vertex cover is by finding a maximal matching in the graph and then taking all of its vertices. It's the same concept, just using another term of graph theory 😊
Another greedy approach for vertex cover that also works pretty well (although a bit less efficient) is repeatedly picking vertices of highest degree.
Nice addition Mario, as always! Actually, I wanted to remove some graph-related examples and to add other examples. I think talking about maximal matching is going too far :)
But you are definitely right! And the other strategy seems good. I just don't know whether it yields a constant-factor approximation. I'd like to think about it and prove it/disprove it.
The other heuristic does not yield a constant-factor approximation. I do not have the proof, but I've read that it can obtain covers that are log n times worse than the optimal.
Mario Cervera
Nice article Jose!
Another way to describe your greedy solution for vertex cover is by finding a maximal matching in the graph and then taking all of its vertices. It's the same concept, just using another term of graph theory 😊
Another greedy approach for vertex cover that also works pretty well (although a bit less efficient) is repeatedly picking vertices of highest degree.