Final answer:
For a recurrence relation of an algorithm with a parameter q greater than 2, if the size of the problem increases polynomials with respect to q, the big O complexity is generally O(n^q).
Step-by-step explanation:
When analyzing the complexity of an algorithm based on a recurrence relation with a parameter q greater than 2, it is essential to know the form of the recurrence. However, if the recurrence describes that the algorithm divides the problem into several subproblems (more than 2) of the same size in each step and if it takes polynomial time to combine these subproblems, we might be dealing with a divide and conquer algorithm with a complexity greater than O(n log n).
For a simple upper bound estimation, if the algorithm's behavior is described by a recurrence where the size of the problem grows polynomial (i.e., the problem size raised to some power q), this suggests that the algorithm's complexity is related to the power to which the problem size is being raised. In this case, the appropriate answer, assuming that the increase in the problem size is the most significant driver of complexity, would be O(n^q).
Without additional context or a specific form of the recurrence relation, providing a precise Big O notation could be speculative. Yet, this explanation would provide a student with a general understanding of how the parameter q affects the asymptotic complexity when the problem size is raised to that power in the recurrence relation.