yes sir, you are correct about lower bound of a Problem. REF
sir, can you confirm the following statement.I think it best describe the confusion between lower bound of a Problem and Lower bound of a particular Algorithm.
Whatever the bound (upper or lower), we are always talking about the worst-case input that we can consider. For example, in sorting, we assume that the worst-case is an unsorted input list.
My understanding is that problems have a lower bound. For example, we say that the lower bound of comparison-based sorting is $\Omega (nlogn)$; we are making no assumptions about what particular comparison-based sorting algorithm we use. Whatever the algorithm (merge sort, quick sort, etc), we cannot do better than this bound of $\Omega(n log n)$. Lower bounds tell us, intuitively, how hard a particular problem is.
When we talk about a specific algorithm, then we talk about upper bounds. For example, we say that the upper bound of bubble sort is $O(n^2)$ and the upper bound of merge sort is $O(n log n)$. Upper bounds, intuitively, tell us how good a particular algorithm is at solving the problem