There have been numerous recent applications of graph databases (e.g., the Semantic Web, ontology representation, social networks, XML, chemical databases, and biological databases). A fundamental structural index for data graphs, namely minimum bisimulation, has been reported useful for efficient path query processing and optimization including selectivity estimation, among many others. Data graphs are subject to change and their indexes are updated accordingly. This paper studies the incremental maintenance problem of the minimum bisimulation of a possibly cyclic data graph. While cyclic graphs are ubiquitous among the data on the web, previous work on the maintenance problem has mostly focused on acyclic graphs. To study the problem with cyclic graphs, we first show that the two existing classes of minimization algorithms - merging algorithm and partition refinement - have their strengths and weaknesses. Second, we propose a novel hybrid algorithm and its analytical model. This algorithm supports an edge insertion or deletion and two forms of batch insertions or deletions. To the best of our knowledge, this is the first maintenance algorithm that guarantees minimum bisimulation of cyclic graphs. Third, we propose to partially reuse the minimum bisimulation before an update in order to optimize maintenance performance. We present an experimental study on both synthetic and real-data graphs that verified the efficiency and effectiveness of our algorithms.

Due to the recent advances in graph databases, a large number of ad-hoc indexes for a fundamental query, in particular, reachability query, have been proposed. The performances of these indexes on different graphs have known to be very different. Worst still, deriving an accurate cost model for selecting the optimal index of a graph database appears to be a daunting task. In this paper, we propose a hierarchical prediction framework, based on neural networks and a set of graph features and a knowledge base on past predictions, to determine the optimal index for a graph database. For ease of presentation, we propose our framework with three structurally distinguishable indexes. Our experiments show that our framework is accurate.