Create an algorithm for the monotonic evaluation function, algorithm A*. Graph G = (V, E); start vertex s; target vertex r; A-Star(G, s, r) in; out: maps as: V V Local: Heuristic lower bound estimate h(u v), open list S, cost function g(u v)

Please show written work with answer!! An independent set in a graph is a set of vertices no two of which are adjacent to each other. A clique is a complete subgraph of a given graph. This means that there is an edge between any two nodes in the subgraph. The maximal clique is the complete subgraph of a given graph which contains the maximum number of nodes. We know that independent set is a NP complete problem. Transform the independent set to max clique (in polynomial time) to show that Max Clique is also NP

Vertex S denotes the start state and vertices G1 and G2 denote the two goal states. Directed edges are labelled with the actual costs of traversing the edge. What path from S to a goal would be found by Iterative deepening Depth-First Search? If all else is equal, consider states in alphabetic order. options are : a. S, A, B, C, D, E, F, G1 b. S, A, B, C, E, F, D, G1 c. S, A, B, C, E, F, G1 d. S, A, B, C, G1 e. S, A, C, G1 f. S, A, E, G1 g. S, B, A, C, E, G1 h. S, B, F, D, G2 i. S, C, B, F, A, D, E, G1 j. S, C, G1

True or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n) <= |h(n)-h(m)|. (b) If an A* heuristics is admissible then it satisfies the monotone restriction. (c) Best-first search guarantees optimality in its returned solution. (d) Least-cost-first search guarantees optimality in its returned solution. (e) If all edges are with unit cost, then Breadth-first search guarantees optimality in its returned solution.