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Regular Path Query Evaluation Sharing a Reduced Transitive Closure Based on Graph Reduction

Inju Na, Ilyeop Yi, Kyu-Young Whang, Yang-Sae Moon, Soon J. Hyun

TL;DR

A novel concept of RPQ-based graph reduction is presented, which significantly simplifies the original graph through edge-level and vertex-level reductions and formally represents the result of an RPQ including a Kleene closure as a relational algebra expression including the RTC.

Abstract

Regular path queries (RPQs) find pairs of vertices of paths satisfying given regular expressions on an edge-labeled, directed multigraph. When evaluating an RPQ, the evaluation of a Kleene closure (i.e., Kleene plus or Kleene star) is very expensive. Furthermore, when multiple RPQs include a Kleene closure as a common sub-query, repeated evaluations of the common sub-query cause serious performance degradation. In this paper, we present a novel concept of RPQ-based graph reduction, which significantly simplifies the original graph through edge-level and vertex-level reductions. Interestingly, RPQ-based graph reduction can replace the evaluation of the Kleene closure on the large original graph to that of the transitive closure to the small reduced graph. We then propose a reduced transitive closure (RTC) as a lightweight structure for efficiently sharing the result of a Kleene closure. We also present an RPQ evaluation algorithm, RTCSharing, which treats each clause in the disjunctive normal form of the given RPQ as a batch unit. If the batch units include a Kleene closure as a common sub-query, we share the lightweight RTC instead of the heavyweight result of the Kleene closure. RPQ-based graph reduction further enables us to formally represent the result of an RPQ including a Kleene closure as a relational algebra expression including the RTC. Through the formal expression, we optimize the evaluation of the batch unit by eliminating useless and redundant operations of the previous method. Experiments show that RTCSharing improves the performance significantly by up to 73.86 times compared with existing methods in terms of query response time.

Regular Path Query Evaluation Sharing a Reduced Transitive Closure Based on Graph Reduction

TL;DR

A novel concept of RPQ-based graph reduction is presented, which significantly simplifies the original graph through edge-level and vertex-level reductions and formally represents the result of an RPQ including a Kleene closure as a relational algebra expression including the RTC.

Abstract

Regular path queries (RPQs) find pairs of vertices of paths satisfying given regular expressions on an edge-labeled, directed multigraph. When evaluating an RPQ, the evaluation of a Kleene closure (i.e., Kleene plus or Kleene star) is very expensive. Furthermore, when multiple RPQs include a Kleene closure as a common sub-query, repeated evaluations of the common sub-query cause serious performance degradation. In this paper, we present a novel concept of RPQ-based graph reduction, which significantly simplifies the original graph through edge-level and vertex-level reductions. Interestingly, RPQ-based graph reduction can replace the evaluation of the Kleene closure on the large original graph to that of the transitive closure to the small reduced graph. We then propose a reduced transitive closure (RTC) as a lightweight structure for efficiently sharing the result of a Kleene closure. We also present an RPQ evaluation algorithm, RTCSharing, which treats each clause in the disjunctive normal form of the given RPQ as a batch unit. If the batch units include a Kleene closure as a common sub-query, we share the lightweight RTC instead of the heavyweight result of the Kleene closure. RPQ-based graph reduction further enables us to formally represent the result of an RPQ including a Kleene closure as a relational algebra expression including the RTC. Through the formal expression, we optimize the evaluation of the batch unit by eliminating useless and redundant operations of the previous method. Experiments show that RTCSharing improves the performance significantly by up to 73.86 times compared with existing methods in terms of query response time.

Paper Structure

This paper contains 19 sections, 6 theorems, 5 equations, 15 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Data Model
  4. Regular Path Query(RPQ)
  5. Evaluation of Multiple RPQs
  6. RPQ-based graph reduction
  7. Edge-Level Graph Reduction (G $\rightarrow$ GR)
  8. Vertex-Level Graph Reduction (GR $\rightarrow$ GR)
  9. Reduced Transitive Closure (RTC)
  10. Reduced Transitive Closure Sharing (RTCSharing)
  11. RTCSharing: an RPQ Evaluation Algorithm
  12. Evaluation of the Batch Unit
  13. Performance Evaluation
  14. Experimental Environment
  15. Performance Evaluation
  16. ...and 4 more sections

Key Result

Lemma 1

R+G is equivalent to TC(GR).

Figures (15)

  • Figure 1: An edge-labeled, directed multigraph.
  • Figure 2: An example of RG.
  • Figure 3: An example of RPQ evaluation.
  • Figure 4: An overview of RPQ-based graph reduction.
  • Figure 5: An example of edge-level reduction.
  • ...and 10 more figures

Theorems & Definitions (24)

  • Definition 1
  • Definition 2
  • Example 1
  • Example 2
  • Example 3
  • Lemma 1
  • proof
  • Example 4
  • Example 5
  • Lemma 2: Pur70
  • ...and 14 more