Question: 6) (40 points) For an undirected graph G = V: E of order n-M, consider the following algorithm: for k 1 to ? for each

6) (40 points) For an undirected graph G = V: E

of order n-M, consider the following algorithm: for k 1 to ?

6) (40 points) For an undirected graph G = V: E of order n-M, consider the following algorithm: for k 1 to ? for each x, y, z in V if (x, z) E E and (z,y) E E then E - E+(x, y) a) What does this algorithm compute? Be specific and concise. b) Determine the best upper bound for k as a function of n. Explain why. Hint: path doubling c) Analyze the running time of the algorithm, using your upper bound for k above d) Find a linear time input enhancement algorithm which solves the same problem. Hint: traverse the graph to number its connected components and explain how to interpret/use those results

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