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Please type in answer QUESTION 5 Estimate the time complexity of Apriori algorithm.

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QUESTION 5

  1. Estimate the time complexity of Apriori algorithm.

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Answer #1

Suppose the number of input transactions is N, the threshold is M, number of unique elements is R. The complexity for generating set of size i is O(R^i) and the time for calculating support for each set can be done in O(n), if using HashMap. Therefore, time complexity would be O[(R + N) + (R^2 + N) + (R^3 + N) …] = O[MN + (R^1+R^2+ … R^M)] = O(MN+ (1-R^M)/(1-R))

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