12Note that in CSPs, the path doesn’t matter, only the solution.3Important things in a graph coloring problem: values (colors), variables (nodes), and the topology of the graph (constraints).Eval is # of pairs attacking queens.4Neighbors are states where one queen has been moved.Hill climbing will try the move that leaves the fewest remaining conflicts. It is a greedy algorithm. Therefore hill climbing doesn’t backtrack, not even for random search between ties. However, you may not want to keep track because a) it takes memory, b) if there are only global maxima/minima, or c) we’re likely to revisit states.Generalize hill climbing algorithm that we used on N-Queens for all CSP’s.5Other methods (DFS, forward search, constraint propagation) did not assign all variables up front.Min-conflicts heuristic - Select variable at random, and then give it the value that results in the fewest conflicts.67If you don’t choose which queen to move randomly, then it is easy to get stuck in a local minimum8(Zebra is a complicated murder mystery-like problem.)9This is why AI is awesome. Because simple ideas produce disturbingly large improvements.MRV is Minimum Remaining ValueDeterministic bias is bad…it is generally much better to choose randomly when choosing which queen to move.10With local search each state is a complete assignment.11How do you generate initial assignment? It is domain specific, though random is generally pretty good.T can be anythingEveryone except T has to be different than SA121314You can really choose any node as the root of the tree.1516After we give V6 a color, the graph can be treated as a tree, where V5 and V3 start 17off with one fewer acceptable colors.Here the complexity of the tree is (N-1 * d^2), done d times, so we have (N-1)*d^3For the HWs/midterm: you should think about these structural ideas, and how the 18algorithms are impacted by structure.1920What you need to
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