show that there exists an instance of the k-means problem for which the k-means algorithm (might) find a solution whose k-means objective is at least t ·

1. Suboptimality of k-Means: For every parameter 1, show that there exists an instance of the k-means problem for which the k-means algorithm (might) find a solution whose k-means objective is at least · OPT, where OPT is the minimum k-means objective.

k-Means Might Not Necessarily Converge to a Local Minimum: Show that the kmeans algorithm might converge to a point which is not a local minimum. Hint: Suppose that = 2 and the sample points are {1,2,3,4} ⊂ R suppose we initialize the k-means with the centers {2,4}; and suppose we break ties in the definition of Ci by assigning to be the smallest value in argminj x−μj       .

find the cost of your paper

Suggest a modification of the binary search algorithm that emulates this strategy for a list of names.

1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

Explain why insertion sort works well on partially sorted lists.

1. Which configuration of data in a list causes the smallest number of exchanges in a selection sort? Which configuration of data causes the largest number of exchanges? 2. Explain….

Draw a class diagram that shows the relationships among the classes in this new version of the system

Jack decides to rework the banking system, which already includes the classes BankView, Bank, SavingsAccount, and RestrictedSavingsAccount. He wants to add another class for checking accounts. He sees that savings….