PRACTICE PROBLEMS

No more homework will be graded, but there are some problems you can work on to help solidify your understanding.

• Explain how to use a solution to the MST decision problem to find an MST of a graph. Hint: First use a binary search to find the weight of the MST, then use self-reducibility to find the set of edges that attains this value.
• CLR Exercise 36.4-6 (pg. 946).
• CLR Exercise 36.4-7 (pg. 946).
• CLR Exercise 36.5-2 (pg. 960).
• Why are those middle nodes needed in the reduction from undirected HAM to directed HAM? What would happen if they were omitted?
• Argue that, in non-metric TSPs, for every ratio r>1, there is no algorithm that can efficiently produce a tour within a ratio bound of r unless P=NP.