Topics 10: Cache Conscious Indexes As main memory gets cheaper, it becomes affordable to build computers with large memories. In future databases all data but few large tables will be memory-resident. Therefore is it important to build efficient main-memory indexes. These indexes should consider the hierarchical memories and the memory-access bottleneck. Dr. N. Mamoulis Advanced Database Technologies

Characteristics of cache conscious indexes They should cluster data according to the access pattern; data that are likely to be accessed together (or in sequence) should be close in memory. They should compress information, so that only useful data are fetched in cache. This means that only comparison keys and reference pointers to searched data should be in the index. They should not be much larger than the indexed information. Dr. N. Mamoulis Advanced Database Technologies

Why is binary search poor? If the searched array is large, the number of cache misses is determined by the search comparisons: O(log2n). This is because from the information fetched in the cache, only one search key will be used. cache-line (128 bytes) Cache: MMem: ... 539 545 568 579 582 589 595 602 609 612 617 623 625 ... current key comparison Dr. N. Mamoulis Advanced Database Technologies

Enhanced Main Memory B+-trees Although the B+-tree is a secondary memory index, it can be used for search in main memory. The node size of the tree is set to a multiple of the cache linesize (e.g., 1 node=2 cachelines). Now the number of cache misses equals the number of tree nodes accessed at search: O(logFn), where F is the fanout of the tree. Dr. N. Mamoulis Advanced Database Technologies

Problems of Main Memory B+-trees Nodes contain as many pointers as key values. Many key values can be compared in a node during search. On the other hand, only one pointer will be followed. Binary search in a node could be expensive (requiring many comparisons) Dr. N. Mamoulis Advanced Database Technologies

The Cache Sensitive Search (CSS) tree Same as B+-tree, but does not store pointers. The children of each node are stored sequentially, thus pointers are induced by positional memory offsets. CSS-tree B+-tree 12 19 31 24 24 12 19 31 4 8 9 12 13 17 19 21 23 24 27 29 31 34 38 4 8 9 12 13 17 19 21 23 24 27 29 31 34 38 Dr. N. Mamoulis Advanced Database Technologies

The Cache Sensitive Search (CSS) tree (cont’d) The CSS tree is suitable only for static data. The capacity of each node is double the capacity of an B+-tree node. Thus the height (and search cost) of the tree is reduced. Another trick used by the CSS tree is hard-coding binary search by if-else statements. Dr. N. Mamoulis Advanced Database Technologies

Hard-coding binary search Normal binary search Binsearch(key,C,start,end)= Binsearch(key,C,mid,end) if key>C[mid] Binsearch(key,C,start,mid) if key<C[mid] Follow C[mid] if key=C[mid]. Augmented binary search if (key<C[mid]) then if (key<C[mid/2]) then ... else if (key>C[mid/2]) then ... else follow C[mid/2] else if (key>C[mid]) then if (key<C[3mid/2]) then ... else if (key>C[3mid/2]) then ... else follow C[3mid/2] else follow C[mid] Dr. N. Mamoulis Advanced Database Technologies

Presentation material A dynamic version of the CSS-tree: the cache conscious B+-tree An improved version of the cache conscious B+-tree (optional reading) Cache conscious R-trees Dr. N. Mamoulis Advanced Database Technologies