Incremental maintenance of the minimum bisimulation of cyclic graphs

Jintian Deng, Byron Choi, Jianliang Xu, Haibo Hu, Sourav S. Bhowmick

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


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.
Original languageEnglish
Article number6361393
Pages (from-to)2536-2550
Number of pages15
JournalIEEE Transactions on Knowledge and Data Engineering
Issue number11
Publication statusPublished - 4 Oct 2013
Externally publishedYes


  • Cyclic graphs
  • evolving graphs and graph algorithms
  • graph indexing
  • incremental maintenance
  • minimum bisimulation

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this