[PPT] - THoSP: an Algorithm for Nesting Property Graphs Giacomo Bergami 1 PowerPoint Presentation

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THoSP: an Algorithm for Nesting Property Graphs

Giacomo Bergami 1 André Petermann 2 Danilo Montesi 1 1st Joint GRADES-NDA International Workshop, 2018 10th June 2018

Università di Bologna1, Universität Leipzig2

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Key Ideas

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Key Ideas – Research Problem

1 An operator allowing to generalize the current “grouping” and

“nesting” is missing. Nevertheless, current (G)DBMSs allow to express nesting operations, but their query languages’ plans do not allow to optimize the whole process by combining the following tasks:

path joins separately for both paterns.
grouping to create an id collection over the matched elements.

2 The general nesting algorithm could lead to an exponential

evaluation time.

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Key Ideas – Use Case

Author Paper∗ authorOf

Vertex Patern

Authorsrc Paper∗ Authorsrc =Authordst Authordst authorOf authorOf

Edge Patern

Author name : Abigail surname : Conner Author name : Baldwin surname : Oliver 1 Author name : Cassie surname : Norman 2 Paper title : On Joining Graphs 3 Paper title : Object Databases 4 Paper title : On Nesting Graphs 5 AuthorOf 6 AuthorOf 7 AuthorOf 8 AuthorOf 9 AuthorOf 10

Input Bibliography Network

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Key Ideas – Desired Result

Paper title : On Joining Graphs 3 Paper title : Object Databases 4 ǫ(0 → 1), ǫ(1 → 0) Paper title : On Nesting Graphs 5 Author name : Abigail surname : Conner ǫ(0) ǫ(0 → 2), ǫ(2 → 0) ǫ(2) Author name : Baldwin surname : Oliver 1 Author name : Cassie surname : Norman 2 coauthorship coauthorship ǫ(1)

Expected result

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Key Ideas – Research Goals

1 As for graph joins, the data model must enhance the

serialization of both operands and graph result.

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Key Ideas – Research Goals

1 As for graph joins, the data model must enhance the

serialization of both operands and graph result.

2 The logical graph nesting operator must be general enough to

support both the THoSP algorithm and other graph summarization tasks.

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Key Ideas – Research Goals

1 As for graph joins, the data model must enhance the

serialization of both operands and graph result.

2 The logical graph nesting operator must be general enough to

support both the THoSP algorithm and other graph summarization tasks.

3 Grouping can be avoided by defining a nesting index, through

which the containment is associated to the container. This can be achieved by extending the Graph Join’s data structures with the aforementioned data structure.

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Logical Model

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Logical Model – Design (1)

The nested (property) graph data model is an extension of the logical model for graph joins. Therefore, we want to preserve the same assumptions: The resulting nested graph is not a materialized view (as in SQL’s SELECT). The nested graph is serialized by only using the ID information. Atribute, values and labels can be completely reconstructed from these informations and the patern rewriting information.

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Logical Model – Design (2)

The following modelling choices allow the reconstruction of the required pieces of information: Vertices and edges are distinctly identified by ids (N2). A nested graph database is a property graph, where each vertex and edge may contain (nest) another property graph (ν, ǫ). Each vertex or edge within the graph can be considered as a possible graph operand.

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Logical Model – Definition

Graph Nesting A nested graph database is a nested graph, where each vertex and edge may represent a graph. Given a nested graph G = (V, E), a vertex patern gV, a edge patern gE vertex patern containing grouping references: ηkeep

ι

(G) =

{ v ∈ V | gV(v) = ∅, keep } ∪ ι(gV(G)),

{ e ∈ E | gE(e) = ∅, keep } ∪ ι(gE(G))

where ι is an indexing function associating to each matched graph into one

new single identifier not appearing in G, and keep is set to true whether the non-traversed vertices and edges must be preserved into the final graph. The newly generated nested graph is inserted into the graph database which also contains G. Values associated to both nested vertices and edges are determined by user defined functions.

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THoSP Algorithm

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THoSP Algorithm – Physical Model

Motivations:

1 Reduce the number of graph visiting times by visiting the

subpatern first, and then extending the visit to the remaining paterns.

2 Represent the nested graph as an adjacency list enriched with

an external nesting index. The algorithm uses the same principles that were adopted for implementing graph joins: Use memory mapping (OS buffering). Serialized graphs represent vertices associated to both ingoing and outgoing edges. No additional indexing structures are exploited.

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THoSP Algorithm – Example

Author name : Abigail surname : Conner Author name : Baldwin surname : Oliver 1 Author name : Cassie surname : Norman 2 Paper title : On Joining Graphs 3 Paper title : Object Databases 4 Paper title : On Nesting Graphs 5 AuthorOf 6 AuthorOf 7 AuthorOf 8 AuthorOf 9 AuthorOf 10

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THoSP Algorithm – Example

Author name : Abigail surname : Conner Author name : Baldwin surname : Oliver 1 Author name : Cassie surname : Norman 2 Paper title : On Joining Graphs 3 Paper title : Object Databases 4 Paper title : On Nesting Graphs 5 AuthorOf 6 AuthorOf 7 AuthorOf 8 AuthorOf 9 AuthorOf 10 Paper title : On Joining Graphs 3