The presence of cycles in a graph makes topological sorting impossible. Topological sorting is designed for directed acyclic graphs (DAGs), and cycles introduce ambiguity in the order of nodes, preventing a clear linear ordering of vertices.

In this scenario, a doubly linked list would be a better choice. The reason is that tasks are added and removed frequently, and a doubly linked list allows for easy insertion and deletion of elements at both the beginning and end of the list, providing efficient operations for a scheduling application.

The optimal substructure property ensures that the solution to a subproblem can be used to solve the original, larger problem. It is a key property for dynamic programming algorithms to efficiently solve problems by breaking them down into smaller subproblems.

Techniques such as transposition and move to front can be implemented to optimize linear search. These techniques involve rearranging elements based on their access patterns, improving the chances of finding the target element early in subsequent searches.

Quick Sort is a divide and conquer sorting algorithm that follows the divide-and-conquer approach. It recursively divides the array into subarrays until each subarray is of size 1 or 0, and then combines them in a sorted manner.

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.

In this scenario, BFS would be the preferable choice. BFS explores neighboring locations first, ensuring that the shortest path is found before moving to more distant locations. It guarantees the shortest route for unweighted graphs, making it suitable for navigation systems. DFS, on the other hand, may find a solution faster in certain cases but does not guarantee the shortest path.

In radix sort, the "radix" or base value is significant as it defines the number of digits in each element. The algorithm processes each digit individually based on this radix, creating a sorted sequence.

Backtracking in DFS involves reverting to the previous step and trying a different option when exploring a solution space. It is particularly useful in problems with multiple decision points and unknown paths.