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Problem. You are given an undirected graph G = (V,E) in which the edge weights are highly restricted.
In particular, each edge has a positive integer weight of either {1, 2, . . . ,W}, where W is a constant (independent of the number of edges or vertices). Show that it is possible to compute the single- source shortest paths in such a graph in O(n + m) time, where n = |V | and m = |E|. (Hint: Because W is a constant, a running time of O(W(n + m)) is as good as O(n + m).)
Requirement: algorithm running time needs to be in DIJKstra's running time or better.
Determine the fundamental period of the following discrete-time signal: X(n) = 2sin(4n)π +π/4) + 5sin16n +4sin (20n +π/3)
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Consider the clique graph below. a) How many subgraphs of G with 3 nodes are there? b) How many of the subgraphs defined in part(a) are induced subgraphs?
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