Given an undirected graph G- (V, E), with V 1,2, -- .n^. A set SC V is a dominating set if every vertex u ? V either belongs to S or is adjacent to a vertex in S. Given a graph, we would like to compute a dominating set of smallest size. Consider the following natural greedy algorithm that attempts to compute a dominating set. Given vEV, let (a) Input G = (V, E). (b) Set D= (e) While V is not empty do let v E V be a vertex with largest degre. . Add v to D. Removev and all vertices in N(v) from G (and thus from V) d) Output D Note: When we remove a vertex incident on r from E. from G, we remove from V, and al edges that are Using appropriate data structures, design an efficient implementation of the above algorithm and analyze/derive the runtime of your implementation. Express the run-time as a function of number of edges (m) and number of vertices (n). Your grade partly depends on efficiency Remark. The above algorithm is a heuristic. It will not always produce a smallest donm inating set. Think about graphs on which the above algorithm fails to produce a smallest dominating set