Decomposing DAGs into spanning trees: A new way to compress transitive closures

Abstract

Let G(V, E) be a digraph (directed graph) with n nodes and e edges. Digraph G* = (V, E*) is the reflexive, transitive closure if (v, u) E* iff there is a path from v to u in G. Efficient storage of G* is important for supporting reachability queries which are not only common on graph databases, but also serve as fundamental operations used in many graph algorithms. A lot of strategies have been suggested based on the graph labeling, by which each node is assigned with certain labels such that the reachability of any two nodes through a path can be determined by their labels. Among them are interval labelling, chain decomposition, and 2-hop labeling. However, due to the very large size of many real world graphs, the computational cost and size of labels using existing methods would prove too expensive to be practical. In this paper, we propose a new approach to decompose a graph into a series of spanning trees which may share common edges, to transform a reachability query over a graph into a set of queries over trees. We demonstrate both analytically and empirically the efficiency and effectiveness of our method.

On the Decomposition of Posets

“…The poset decomposition is quite useful in practice. As shown in [4], if we can decompose a DAG G into a minimum set of chains, the transitive closure [24] of G can be effectively compressed to support the so-called reachability queries [5,6].…”

A Survey on Graph Database Management Techniques for Huge Unstructured Data

“…It is capable of dealing with complex relationship requiring multiple hops. It provides graph-wise indexes on multiple key fields and also provides high performance regarding query [7], [10].…”

“…Bug Localization is another application area worth mentioning for the use of graph databases. Overall there is a variety of domains where graph data modeling can be applied to revolutionize the user experience [7].…”

“…Neo4j also supports another language like Python except for Java for graph operations. Neo4j is an open source project [7] available in a GPLv3 Community edition, with Advanced and Enterprise editions available under both the AGPLv3 as well as a commercial license. Neo4j is best graph database for enterprise deployment.…”

Reachability querying: an independent permutation labeling approach

“…The real applications that need this operation are many and can be found among online social networks, biological networks, ontology, transportation networks, etc. The reachability query has been extensively studied over a decade [1,16,13,23,11,28,7,26,12,8,21,20,29,27,9,10,19,24,31], and the early work can be traced back to 1989 to compute transitive closure (TC) over a graph. However, it is still an unsolved question whether we can do faster to answer reachability queries online over even larger and/or even denser graphs with the possible minimum cost (time/space) for offline precomputing and preparation.…”