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Question :
(a) Suppose that you are given an instance of the MST problem on a graph G, with edge weights that are all positive and distinct. Let T be the minimum spanning tree for G returned by Kruskal's algorithm. Now suppose we replace each edge weight w_e by its square w2_e, thereby creating a new instance of the problem with the same graph but different edge weights. Is it true that T is still a minimum spanning tree for this new instance. If you think it is true, give an explanation; otherwise, give a counterexample.
(b) Let G = (V, E) e a directed graph in which every edge has unit length (i.e., length = 1). Design an algorithm that given any two vertices s and t of G, find a shortest path from s to t using O(|E|) time.
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A movie theatre is considering the purchase of a new three-dimensional (3D) digital projection system. The new ticket price for a 3D movie will be $15.
Modify the program we discussed and executed in class to use functions to calculate the sum, product, difference and quotient of two 4 element.
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Some Shewhart charts include warning limits, which are between the mean and the control limits. Discuss reasonable values for the warning limits.
Refer to Problem. Use a spreadsheet to extend the number of trials to 500. Compute E(AW) and plot the cumulative average AW.
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