Optimizing multidimensional index trees for main memory access

Abstract

Recent studies have shown that cache-conscious indexes such as the CSB+-tree outperform conventional main memory indexes such as the T-tree. The key idea of these cache-conscious indexes is to eliminate most of child pointers from a node to increase the fanout of the tree. When the node size is chosen in the order of the cache block size, this pointer elimination effectively reduces the tree height, and thus improves the cache behavior of the index. However, the pointer elimination cannot be directly applied to multidimensional index structures such as the R-tree, where the size of a key, typically, an MBR (minimum bounding rectangle), is much larger than that of a pointer. Simple elimination of fourbyte pointers does not help much to pack more entries in a node. This paper proposes a cache-conscious version of the R-tree called the CR-tree. To pack more entries in a node, the CR-tree compresses MBR keys, which occupy almost 80% of index data in the two-dimensional case. It first represents the coordinates of an MBR key relatively to the lower left corner of its parent MBR to eliminate the leading 0's from the relative coordinate representation. Then, it quantizes the relative coordinates with a fixed number of bits to further cut off the trailing less significant bits. Consequently, the CR-tree becomes significantly wider and smaller than the ordinary R-tree. Our experimental and analytical study shows that the two-dimensional CR-tree performs search up to 2.5 times faster than the ordinary R-tree while maintaining similar update performance and consuming about 60% less memory space.

An efficient cache conscious multi-dimensional index structure

“…Two kinds of data set such as uniformly distributed syn- thetic data set and real data set (TIGER) were used in the experiments. The generation method of the uniform distribution data sets is the same as that of the uniform distribution data sets in CR-tree [8]. First we generated integers between 0 and 100 by using random number generator and stored them to a 2-dimensional array sequentially.…”

“…However, when the number of bits used in compression is 4, the performance of CR-tree is almost same to that of PR-tree. As mentioned in [8], the number of compression bits affects the performance of CR-tree. In our experiments, 8 bit compression shows best performance.…”

“…Subsequently, several researches to improve the performance of index structures for MMDBMS by reducing L2 cache misses have been done actively in the database community [6,7,9,11,8,5]. Since the end of 1990s, cache conscious index structures have been one of the primary concerns to improve the performance of MMDBMSs.…”

“…To our knowledge, representative cache conscious multi-dimensional index structures are cache conscious R-tree (CR-tree) [8], partial R-tree (PR-tree) [5] and normal R-tree [2] with a small node size, a cache line size or its multiple. CR-trees compress MBR keys by quantizing coordinate values to the fixed number of bits.…”

Indexing high-dimensional data for main-memory similarity search

“…A number of index structures have been proposed for main memory query processing [21,17,8], built upon the idea of packing the index into pages that can fit in the cache line, the size of which usually ranges from 32 to 128 bytes. However, these indexes are designed for single or low-dimensional data and are not suitable for highdimensional data.…”