Question: Problem : Describe reasonable heuristic algorithms or rules for the follow- ing problems. For this problem, you do not need to give full implementation details:

Problem : Describe reasonable heuristic algorithms or rules for the follow- ing problems. For this problem, you do not need to give full implementation details: it is enough to describe the main idea behind the algorithm or rule in 1-2 sentences. Keep in mind that it is ok if a heuristic sometimes fails to find the best answer.

The Graph Coloring problem is as follows: Given a graph G, we want to assign each node a `color' such that if two nodes are adjacent (connected), then they do not have the same color. For example, if you are coloring countries on a map, then two countries that share a border should have different colors. The goal of this problem is to determine the smallest number of colors required to accomplish this. This problem is known to be NP-Complete. Design a reasonable heuristic algorithm for determining the number of colors needed to color the vertices so that no two adjacent vertices have the same color.

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