Cache-oblivious algorithms are a class of algorithms that optimize for data locality without knowledge of the cache size or block size of a particular computer system. These algorithms are designed to work well on a wide range of memory hierarchies, including modern multi-level caches and disks, by using recursive subproblems with small subarrays that fit in cache, while minimizing the number of I/O operations.
One of the most widely used cache-oblivious algorithms is the cache-oblivious matrix transpose algorithm. The algorithm recursively partitions the matrix into smaller submatrices until each submatrix fits in cache, then transposes each submatrix in place, taking advantage of cache locality. The algorithm runs in O(n2/B + nlog _BN) I/Os and O(n2) time, where n is the matrix size, B is the block size, and N is the cache size.
Cache-oblivious algorithms have also been developed for other problems, such as sorting, searching, and graph algorithms. For example, the cache-oblivious binary search algorithm is a modification of the classical binary search algorithm that recursively partitions the array into smaller subarrays that fit in cache, using the same strategy as the matrix transpose algorithm. The algorithm runs in O(log _Bn) memory transfers and O(log n) time, where n is the size of the array and B is the block size.
Cache-oblivious algorithms have been shown to be competitive with cache-aware algorithms in practice, while providing theoretical guarantees on performance for a wide range of memory hierarchies. They are particularly useful for problems that involve large datasets that do not fit in main memory, such as in database management, scientific computing, and data analysis.