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Consider an undirected graph G = (Viz, Eg). A vertex cover is a subset S C Vi such that every edge in E¢ is incident to at least one vertex in S.
Question 1. Explain how to construct a Markov random field to represent the uniform probability distri- bution, p, over valid vertex covers of G.
Question 2. Explain why your construction always yields a valid probability distribution.
Question 3. Let GG be the graph consisting of a single cycle on four nodes. What is the partition function (normalizing constant) of the MRF for this choice of G?
Question 4. Explain how to construct an MRF to represent a probability distribution over vertex covers such that for all vertex covers S, p(S)
Binary search tree, and postorder and preorder traversal Determine the shortest path in Graph
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