The Fibonacci sequence is an integer sequence where each term is the sum of the two preceding ones, starting from 0 and 1. It exhibits exponential growth and has numerous applications in nature, art, and algorithms, making it a fascinating mathematical concept.

The primary purpose of Dijkstra's algorithm is to find the shortest path between two nodes in a graph, particularly in a graph with non-negative edge weights. It is commonly used in routing and network protocols.

Linear search performs better on sorted arrays. This is because, in a sorted array, once a value greater than the target is encountered, the search can stop, resulting in early termination. On the other hand, in an unsorted array, the search continues until the target is found or the entire array is traversed.

BFS explores all nodes at the same level before moving to the next level. This ensures that the algorithm covers all nodes at a particular level before proceeding to the subsequent level in a graph traversal.

In Kruskal's algorithm, a Disjoint Set, also known as Union-Find, is commonly used to efficiently determine if adding an edge will create a cycle in the graph. This data structure helps in maintaining disjoint sets and quickly checking whether two vertices belong to the same set, enabling the algorithm to avoid adding edges that would create cycles.

Edit Distance is crucial in spell checking, where it helps identify and correct misspelled words by calculating the minimum number of operations (insertions, deletions, substitutions) required to transform one word into another.

The Knuth-Morris-Pratt (KMP) algorithm utilizes a failure function (also known as the longest prefix suffix array) to optimize the search process. The failure function is precomputed based on the pattern and helps the algorithm determine the maximum length of a proper suffix that matches a proper prefix within the pattern. This information is then used to efficiently skip unnecessary comparisons during the search.

Metacharacters in regular expressions are special characters that provide a specific meaning to a search pattern. They allow for more flexible and powerful matching by representing concepts like repetition, alternatives, and grouping in the pattern.

In this scenario, Manacher's Algorithm would be the preferred choice. It has a linear time complexity and is specifically designed for finding the Longest Palindromic Substring efficiently, making it suitable for large strings.

Computational challenges include dealing with integer overflow, handling precision issues with floating-point arithmetic, and optimizing recursive approaches. Strategies may involve memoization to store and reuse previously computed results, optimizing algorithms for better efficiency, and considering alternative data types for large values of n.