Before revision: We study the classical online bipartite matching problem: One side of the graph is known and vertices of the other side arrive online. It is well known that when the graph is edge-weighted , and vertices arrive in an adversarial order, no online algorithm has a nontrivial competitive-ratio.
After revision: We study the greedy-based online algorithm for edge-weighted , and vertices arrive in an adversarial order, no online algorithm has a nontrivial competitive-ratio.