Gavrilov's Algorithm is a method used in computer science for solving the problem of finding the longest common subsequence (LCS) between two sequences. The algorithm efficiently identifies the longest sequence that can be derived from both original sequences without rearranging their elements. This is particularly useful in fields like bioinformatics, where comparing DNA or protein sequences is essential. The algorithm operates by constructing a matrix that represents the lengths of common subsequences at various points in the two sequences. By filling in this matrix and backtracking, Gavrilov's Algorithm can determine the LCS, providing valuable insights into the similarities and differences between the sequences being analyzed.