Dwarf: shrinking the PetaCube

Abstract

Dwarf is a highly compressed structure for computing, storing, and querying data cubes. Dwarf identifies prefix and suffix structural redundancies and factors them out by coalescing their store. Prefix redundancy is high on dense areas of cubes but suffix redundancy is significantly higher for sparse areas. Putting the two together fuses the exponential sizes of high dimensional full cubes into a dramatically condensed data structure. The elimination of suffix redundancy has an equally dramatic reduction in the computation of the cube because recomputation of the redundant suffixes is avoided. This effect is multiplied in the presence of correlation amongst attributes in the cube. A Petabyte 25-dimensional cube was shrunk this way to a 2.3GB Dwarf Cube, in less than 20 minutes, a 1:400000 storage reduction ratio. Still, Dwarf provides 100% precision on cube queries and is a self-sufficient structure which requires no access to the fact table. What makes Dwarf practical is the automatic discovery,in a single pass over the fact table, of the prefix and suffix redundancies without user involvement or knowledge of the value distributions.This paper describes the Dwarf structure and the Dwarf cube construction algorithm. Further optimizations are then introduced for improving clustering and query performance. Experiments with the current implementation include comparisons on detailed measurements with real and synthetic datasets against previously published techniques. The comparisons show that Dwarfs by far out-perform these techniques on all counts: storage space, creation time, query response time, and updates of cubes.