We define a shortest path algorithm to be oblivious if
given a graph G=(V,E), with vertices numbered 1..n, it decides to a
execute a series of relax statements based only the values n = |V| and
m = |E|, and not based on the particular structure of the graph. For
example, Bellman-Ford algorithm is oblivious, but Dijkstra's algorithm is not.
Prove the following statement: Any oblivious algorithm that correctly computes single source shortest paths for all graphs G, must have a worst-case running time of Ω(nm).