A Reachability Index for Recursive Label-Concatenated Graph Queries

Abstract

Reachability queries checking the existence of a path from a source node to a target node are fundamental operators for querying and processing graph data. Current approaches for index-based evaluation of reachability queries either focus on plain reachability or constraint-based reachability with alternation only. In this paper, for the first time we study the problem of index-based processing for recursive label-concatenated reachability queries, referred to as RLC queries. These queries check the existence of a path that can satisfy the constraint defined by a concatenation of at most 𝑘 edge labels under the Kleene plus. Many practical graph database and network analysis applications exhibit RLC queries. However, their evaluation remains prohibitive in current graph database engines.We introduce the RLC index, the first reachability index to efficiently process RLC queries. The RLC index checks whether the source vertex can reach an intermediate vertex that can also reach the target vertex under a recursive label-concatenated constraint. We propose an indexing algorithm to build the RLC index, which guarantees the soundness and the completeness of query execution and avoids recording redundant index entries. Comprehensive experiments on real-world graphs show that the RLC index can significantly reduce both the offline processing cost and the memory overhead of transitive closure while improving query processing up to six orders of magnitude over online traversals. Finally, our opensource implementation of the RLC index significantly outperforms current mainstream graph engines for evaluating RLC queries.

An Overview of Reachability Indexes on Graphs

“…Figure 1(b) shows an edge-labeled graph, representing a social network with three kinds of relationships, i.e., 𝐿 = {friendOf, follows, worksFor}. Reachability queries over edge-labeled graphs can be expressed with additional constraints on paths using edge labels [21,52], referred to as path-constrained reachability queries. A pathconstrained reachability query 𝑄 𝑟 (𝑠, 𝑡, 𝛼) contains as arguments source (𝑠) and target (𝑡) vertices, and an expression 𝛼 specifying the path constraint using 𝐿. 𝑄 𝑟 (𝑠, 𝑡, 𝛼) checks whether there exists an 𝑠-𝑡 path in 𝐺 such that the path can satisfy the constraint enforced by 𝛼.…”

“…The naive approach to accelerate plain reachability queries is to build a transitive closure (TC) [2], which can be extended to path-constrained reachability queries, called generalized transitive closure (GTC) [21,52]. TC computes and stores the existence of a path between every pair of vertices in the graph.…”

“…The derivation process should take much less time than the query processing using online graph traversal, which makes indexes interesting. There exist two different types of reachability indexes that mirror the reachability queries: plain reachability indexes [2, 7-9, 11, 13, 14, 17-20, 25-27, 29, 31, 34, 35, 39-41, 43, 45, 46, 49-51, 55] and path-constrained reachability indexes [10,12,21,33,44,52,56].…”

“…The problem of indexing concatenation-based reachability queries is first studied by Zhang et al [52] which proposes the RLC index. To index such queries, the minimum repeats (MR) of edge-label sequence are recorded, e.g., the MR of the path (L, worksFor, D, friendOf, H, worksFor, G, friendOf, B) is (worksFor, friendOf), and the MR is helpful in processing 𝑄 𝑟 (𝐿, 𝐵, worksFor•friendOf) * ).…”

“…As noted above, in real-world graphs, it is likely that there will be many vertices that might not be reachable from a given source vertex, and, therefore, it would be interesting to have a partial index without false negatives for path-constrained reachability queries. Equally importantly, we observe that the index construction cost of path-constrained reachability indexes is high and takes hours of indexing for graphs with millions of vertices [10,12,33,52]. This also calls for the design of partial indexes without false negatives.…”