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Evaluating Continuous Basic Graph Patterns over Dynamic Link Data Graphs

Manolis Gergatsoulis, Matthew Damigos

TL;DR

This work addresses the problem of continuously evaluating Basic Graph Patterns over dynamic Linked Data graphs that update via an unbounded stream of insertions and deletions. It introduces a decomposition-based, in-memory framework that maintains delta embeddings by splitting BGPs into subqueries (ground, simple var-centric star, loosely-connected, and var-connected) and combining intermediate results. The authors establish polynomial time and space guarantees for delta embedding computation, with particularly efficient handling for ground and simple var-centric cases, and they develop a hierarchical approach for more complex var-connected queries. The approach supports real-time delta answers as updates arrive and highlights avenues for future work in distributed settings and ML-assisted optimization to further accelerate evaluation on streaming RDF data.

Abstract

In this paper, we investigate the problem of evaluating Basic Graph Patterns (BGP, for short, a subclass of SPARQL queries) over dynamic Linked Data graphs; i.e., Linked Data graphs that are continuously updated. We consider a setting where the updates are continuously received through a stream of messages and support both insertions and deletions of triples (updates are straightforwardly handled as a combination of deletions and insertions). In this context, we propose a set of in-memory algorithms minimizing the cached data to efficiently and continuously answer BGP queries. The queries are typically submitted into a system and continuously result in the delta answers while the update messages are processed. To efficiently and continuously evaluate the submitted query over the streaming data, as well as to minimize the amount of cached data, we propose an approach where the submitted query is decomposed into simpler subqueries and the query evaluation is achieved by combining the intermediate answers of the subqueries. Using this approach, the proposed algorithms compute the delta answers of a BGP query in polynomial time and space. Note that for certain subclasses of BGP queries, we show that the evaluation can be achieved in constant or linear time and space. Consolidating all the historical delta answers, the algorithms ensure that the answer to each query is constructed at any given time.

Evaluating Continuous Basic Graph Patterns over Dynamic Link Data Graphs

TL;DR

This work addresses the problem of continuously evaluating Basic Graph Patterns over dynamic Linked Data graphs that update via an unbounded stream of insertions and deletions. It introduces a decomposition-based, in-memory framework that maintains delta embeddings by splitting BGPs into subqueries (ground, simple var-centric star, loosely-connected, and var-connected) and combining intermediate results. The authors establish polynomial time and space guarantees for delta embedding computation, with particularly efficient handling for ground and simple var-centric cases, and they develop a hierarchical approach for more complex var-connected queries. The approach supports real-time delta answers as updates arrive and highlights avenues for future work in distributed settings and ML-assisted optimization to further accelerate evaluation on streaming RDF data.

Abstract

In this paper, we investigate the problem of evaluating Basic Graph Patterns (BGP, for short, a subclass of SPARQL queries) over dynamic Linked Data graphs; i.e., Linked Data graphs that are continuously updated. We consider a setting where the updates are continuously received through a stream of messages and support both insertions and deletions of triples (updates are straightforwardly handled as a combination of deletions and insertions). In this context, we propose a set of in-memory algorithms minimizing the cached data to efficiently and continuously answer BGP queries. The queries are typically submitted into a system and continuously result in the delta answers while the update messages are processed. To efficiently and continuously evaluate the submitted query over the streaming data, as well as to minimize the amount of cached data, we propose an approach where the submitted query is decomposed into simpler subqueries and the query evaluation is achieved by combining the intermediate answers of the subqueries. Using this approach, the proposed algorithms compute the delta answers of a BGP query in polynomial time and space. Note that for certain subclasses of BGP queries, we show that the evaluation can be achieved in constant or linear time and space. Consolidating all the historical delta answers, the algorithms ensure that the answer to each query is constructed at any given time.
Paper Structure (17 sections, 11 theorems, 4 equations, 5 figures, 3 tables, 7 algorithms)

This paper contains 17 sections, 11 theorems, 4 equations, 5 figures, 3 tables, 7 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Preliminaries
  4. Data and query graphs
  5. Data and query graph decomposition
  6. Embeddings and query answers
  7. Special forms of queries and query decomposition
  8. Special forms of queries
  9. Connected-variable and star decompositions of BGP queries
  10. Continuous pattern matching
  11. Answering BGP queries over dynamic Linked Data
  12. A generic query evaluation procedure
  13. Evaluating ground BGP queries
  14. Evaluating simple var-centric star queries
  15. Evaluating loosely-connected BGP queries
  16. ...and 2 more sections

Key Result

Lemma 1

Let $Q$ be a loosely-connected BGP query and ${\cal D_{CV}}(Q)$ be the connected-variable decomposition of $Q$. Then each non-ground query in ${\cal D_{CV}}(Q)$ is a simple var-centric star query.

Figures (5)

  • Figure 1: Connected-variable decomposition of a BGP query $Q$.
  • Figure 2: Connected-variable decomposition of a loosely connected BGP query $Q$.
  • Figure 3: Var-connected queries - Recursive decomposition
  • Figure 4: a) Var-connected star decomposition of a query Q1, b) Overlapping-subqueries graph.
  • Figure 5: Example - Evaluation of a var-connected query (Insertion).

Theorems & Definitions (28)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • Definition 10
  • ...and 18 more