Big-Omega (Ω) notation is a fundamental concept in algorithm analysis, used to describe the lower bound of an algorithm's time or space complexity. It signifies the best-case scenario for an algorithm's performance, indicating that the algorithm will take at least a certain amount of time or space to complete, regardless of the input.

Formally, a function $f(n)$ is said to be in $\Omega(g(n))$ if there exist positive constants $c$ and $n_0$ such that $f(n) \ge c \cdot g(n)$ for all $n \ge n_0$. In simpler terms, for sufficiently large input sizes ($n \ge n_0$), the function $f(n)$ is always greater than or equal to some positive constant multiple ($c$) of $g(n)$.

An algorithm is $\Theta(g(n))$ if and only if it is both $O(g(n))$ and $\Omega(g(n))$. This means the algorithm's performance is tightly bounded by $g(n)$ in all cases.

Consider a linear search algorithm. In the best case, the element we are looking for is the first element in the array. In this scenario, the algorithm only needs to perform one comparison. Therefore, the best-case time complexity is constant, which can be expressed as $\Omega(1)$.

For a sorting algorithm like Bubble Sort, even if the array is already sorted, it will still iterate through the entire array multiple times to confirm it's sorted. However, its best-case scenario (already sorted array) requires $n$ comparisons and $n-1$ swaps, leading to a time complexity of $\Omega(n)$.

Understanding Big-Omega is crucial for GATE CS because it helps in:

1. Identifying Optimal Algorithms: Knowing the lower bound helps in comparing different algorithms and selecting the most efficient one for a given problem.
2. Understanding Problem Complexity: It provides insights into the inherent difficulty of a problem, regardless of the algorithm used.
3. Analyzing Best-Case Scenarios: Many competitive programming problems have specific test cases that might trigger an algorithm's best-case behavior, making Ω analysis vital.

Always remember that Big-Omega represents the best-case scenario. When analyzing algorithms, consider the input that allows the algorithm to finish as quickly as possible. This is the foundation for understanding the lower bounds of computational tasks.