Question

Which of the following statements about the complexity of the greedy modularity maximization algorithm is TRUE :

a. The algorithm always performs N community mergings.
b. For a dense graph the run time complexity is O(N ∧ 2)
c. With appropriate data-structures the run time complexity can be reduced to O(NlogN)
d. Inspecting each link and then computing the modularity difference requires O(L ∗ K) computations, where L is the number of links and K is the number of operations to calculate the modularity difference.

Answer 1

Statement (c), which asserts that the run time complexity of the greedy modularity maximization algorithm can be reduced to O(NlogN) with appropriate data structures, is true.

Step-by-step explanation:

The complexity of the greedy modularity maximization algorithm is related to community detection in networks within the field of computational science. When examining the statements provided:

• (a) is not necessarily true as the number of community mergings can vary.
• (b) is incorrect since the run time complexity is stated as O(N²) which might be true for a brute force approach but is not the complexity of the greedy algorithm itself.
• (c) is true because with the use of appropriate data structures, such as a heap or balanced tree, the run time complexity can indeed be reduced to O(NlogN).
• (d) is not accurate as the computation required is not described as O(L * K) in the context of greedy modularity maximization.

In conclusion, the statement (c) 'With appropriate data-structures the run time complexity can be reduced to O(NlogN)' is TRUE.