Question: Algorithms - Dynamic Programming Let graph G = (V,E) be a path with n vertices v1,v2,....,vn, and n-1 edges (vi,vi+1), 1

Algorithms - Dynamic Programming

Let graph G = (V,E) be a path with n vertices v1,v2,....,vn, and n-1 edges (vi,vi+1), 1 <= i <= n-1. On each vertex vi there is a positive integer weight wi. A subset of vertices is independent if there is no edge between any pair of vertices in the subset. The weight of a subset is the sum of the weights on its vertices. Design an efficient dynamic programming algorithm to find a maximum weight independent set in G and analyze the complexity of your algorithm. Describe the subproblems that you use in your dynamic programming solution and show the underlying DAG.

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