2. Let G (V, E) be an undirected graph with V-[1,2, .. ,n]. Given a vertex r, let A subset S S V is called independent if for every pair of distinct vertices x,y from S, the following holds: A set SCV is called mazimal independent if S is independent and for every y S, SU is not independent Design an algorithm that gets an undirected graph G (V, E) and a subset S CV as input and determines if S is independent or not. You may assume V 1,2,.. ,n] Derive the run-time of your algorithm. Part of your grade depends on the run-time. Design an algorithm that gets a graph G (V, E) as input and outputs a maximal independent set of G. Derive the run-time of your algorithm. Your grade partly depends on the run-time. You may assume V 1,2, -. ,n 2. Let G (V, E) be an undirected graph with V-[1,2, .. ,n]. Given a vertex r, let A subset S S V is called independent if for every pair of distinct vertices x,y from S, the following holds: A set SCV is called mazimal independent if S is independent and for every y S, SU is not independent Design an algorithm that gets an undirected graph G (V, E) and a subset S CV as input and determines if S is independent or not. You may assume V 1,2,.. ,n] Derive the run-time of your algorithm. Part of your grade depends on the run-time. Design an algorithm that gets a graph G (V, E) as input and outputs a maximal independent set of G. Derive the run-time of your algorithm. Your grade partly depends on the run-time. You may assume V 1,2, -. ,n