Parallel Hierarchical Evaluation of Tranitive Closure Queries

This paper presents a new approach to parallel computation of transitive closure queries using a semantic data fragmentation. We assume that tuples of a large base relation denote edges in a graph, which models a transportation network; we propose a fragmentation algorithm which produces the partitioning of the base relation into several fragments such that any fragment corresponds to a subgraph. Any two fragments are considered as either adjacent or nonadjacent; two fragments are adjacent when the corresponding subgraphs have a nonempty intersection. One fragment, called high-speed fragment, collects all edges which guarantee maximum speed, these edges correspond to highways or to high-speed inter-city trains. Thus, the fragmentation algorithm induces a hierarchical relationship between the high-speed fragment and all other fragments. With this fragmentation, any query about paths connecting two nodes can be answered by using just the fragments in which nodes are located and the high-speed fragment. In general, if each fragment is managed by a distinguished processor, then the query can be answered by three processors working in parallel. This schema can be recursively applied to generate an arbitrary number of hierarchical levels.