While considering data structure implementation, the factor(s) under consideration is (are):

When implementing a data structure, several factors need to be considered:

1. Memory Usage: Different data structures use different amounts of memory. For example, arrays require a contiguous block of memory, while linked lists do not. The choice of data structure can significantly impact the memory usage of your program.

2. Speed of Operations: Different data structures have different time complexities for various operations. For example, accessing an element in an array is a constant time operation, while it is a linear time operation in a linked list. The choice of data structure can significantly impact the speed of your program.

3. Ease of Implementation: Some data structures are easier to implement than others. For example, arrays are generally easier to implement than binary trees. The choice of data structure can significantly impact the development time of your program.

4. Flexibility: Some data structures are more flexible than others. For example, the size of an array is fixed at the time of creation, while the size of a linked list can change dynamically. The choice of data structure can significantly impact the flexibility of your program.

5. Specific Requirement: Depending on the specific requirements of your program, you might need to use a specific data structure. For example, if you need to frequently access elements in the middle of the list, a linked list might be a better choice than an array.

So, the factors under consideration while implementing a data structure are memory usage, speed of operations, ease of implementation, flexibility, and specific requirements.