The choice between AVL and red-black trees often depends on the functional characteristics of the application and the frequency of the operations being performed. AVL trees tend to have a more balanced structure, suitable for scenarios where search operations are frequent, while red-black trees might be preferred for scenarios with more frequent insertion and deletion operations.

In bubble sort, where each iteration places the largest unsorted element to its correct position, n-1 iterations are required to sort an array of size n, making a total of (n-1) + (n-2) + ... + 1 iterations.

Breadth-First Search (BFS) explores nodes level by level, starting from the source node and moving to their neighbors. It systematically visits all the neighbors at the current depth before moving on to nodes at the next level.

The bottom-up approach is commonly used in dynamic programming to efficiently compute Fibonacci numbers. It involves solving smaller subproblems first and using their solutions to build up to the solution of the original problem, often utilizing an array or table to store intermediate results.

"Increasing" in the Longest Increasing Subsequence (LIS) problem refers to arranging elements in ascending order. The goal is to find the longest subsequence where elements are in increasing order.

Linear search is a versatile algorithm that can be applied to search for elements, values, or objects in collections other than arrays. It is not limited to specific data types and can be used in various scenarios for searching unsorted data.

Adapting BFS for a maze with obstacles can be done by incorporating a heuristic approach, similar to A* Algorithm. A* considers both the cost to reach a point and an estimate of the remaining distance to the goal. In the context of a maze, this modification helps BFS navigate efficiently around obstacles, making it more effective for pathfinding in complex environments compared to the traditional BFS approach.

When sorting large datasets stored on disk, mitigating the risk of running out of memory involves using an in-memory caching mechanism. This mechanism allows frequently accessed data to be stored in memory, reducing disk I/O operations and minimizing the chance of memory exhaustion.

In the context of LCS, a subsequence is a sequence of elements that appear in the same order as in the original sequence but not necessarily consecutively. It allows for gaps between elements in the subsequence.

Radix sort involves sorting elements based on individual digits. Starting from the least significant digit (LSD) to the most significant digit (MSD), elements are grouped and rearranged. The process is repeated until all digits are considered, resulting in a sorted array. Pseudocode and implementation details provide a clearer understanding.