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From "Vasia Kalavri (JIRA)" <j...@apache.org>
Subject [jira] [Resolved] (FLINK-2411) Add basic graph summarization algorithm
Date Mon, 26 Oct 2015 10:46:27 GMT

     [ https://issues.apache.org/jira/browse/FLINK-2411?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]

Vasia Kalavri resolved FLINK-2411.
----------------------------------
       Resolution: Implemented
    Fix Version/s: 1.0

> Add basic graph summarization algorithm
> ---------------------------------------
>
>                 Key: FLINK-2411
>                 URL: https://issues.apache.org/jira/browse/FLINK-2411
>             Project: Flink
>          Issue Type: New Feature
>          Components: Gelly
>    Affects Versions: 0.10
>            Reporter: Martin Junghanns
>            Assignee: Martin Junghanns
>            Priority: Minor
>             Fix For: 1.0
>
>
> Graph summarization determines a structural grouping of similar vertices and edges to
condense a graph and thus helps to uncover insights about patterns hidden in the graph. It
can be used in OLAP-style operations on the graph and is similar to group by in SQL but on
the graph structure instead of rows.
>  
> The graph summarization operator represents every vertex group by a single vertex in
the summarized graph; edges between vertices in the summary graph represent a group of edges
between the vertex group members of the original graph. Summarization is defined by specifying
grouping keys for vertices and edges, respectively.
> One publication that presents a Map/Reduce based approach is "Pagrol: Parallel graph
olap over large-scale attributed graphs", however they pre-compute the graph-cube before it
can be analyzed. With Flink, we can give the user an interactive way of summarizing the graph
and do not need to compute the  cube beforehand.
> A more complex approach focuses on summarization on graph patterns  "SynopSys: Large
Graph Analytics in the SAP HANA Database Through Summarization".
> However, I want to start with a simple algorithm that summarizes the graph on vertex
and optionally edge values and additionally stores a count aggregate at summarized vertices/edges.
> Consider the following two examples (e.g., social network with users from cities and
friendships with timestamp):
>  
> h4. Input graph:
>  
> Vertices (id, value):
> (0, Leipzig)
> (1, Leipzig)
> (2, Dresden)
> (3, Dresden)
> (4, Dresden)
> (5, Berlin)
> Edges (source, target, value):
> (0, 1, 2014)
> (1, 0, 2014)
> (1, 2, 2013)
> (2, 1, 2013)
> (2, 3, 2014)
> (3, 2, 2014)
> (4, 0, 2013)
> (4, 1, 2015)
> (5, 2, 2015)
> (5, 3, 2015)
> h4. Output graph (summarized on vertex value):
> Vertices (id, value, count)
> (0, Leipzig, 2) // "2 users from Leipzig"
> (2, Dresden, 3) // "3 users from Dresden"
> (5, Berlin, 1) // "1 user from Berlin"
> Edges (source, target, count) 
> (0, 0, 2) // "2 edges between users in Leipzig"
> (0, 2, 1) // "1 edge from users in Leipzig to users in Dresden"
> (2, 0, 3) // "3 edges from users in Dresden to users in Leipzig"
> (2, 2, 2) // "2 edges between users in Dresden"
> (5, 2, 2) // "2 edges from users in Berlin to users in Dresden"
> h4. Output graph (summarized on vertex and edge value):
> Vertices (id, value, count)
> (0, Leipzig, 2)
> (2, Dresden, 3)
> (5, Berlin, 1)
> Edges (source, target, value, count) 
> (0, 0, 2014, 2) // ...
> (0, 2, 2013, 1) // ...
> (2, 0, 2013, 2) // "2 edges from users in Dresden to users in Leipzig with timestamp
2013"
> (2, 0, 2015, 1) // "1 edge from users in Dresden to users in Leipzig with timestamp 2015"
> (2, 2, 2014, 2) // ...
> (5, 2, 2015, 2) // ...
> I've already implemented two versions of the summarization algorithm in our own project
[Gradoop|https://github.com/dbs-leipzig/gradoop], which is a graph analytics stack on top
of Hadoop + Gelly/Flink with a fixed data model. You can see the current WIP here: 
> 1 [Abstract summarization|https://github.com/dbs-leipzig/gradoop/blob/%2345_gradoop_flink/gradoop-flink/src/main/java/org/gradoop/model/impl/operators/Summarization.java]
> 2 [Implementation using cross|https://github.com/dbs-leipzig/gradoop/blob/%2345_gradoop_flink/gradoop-flink/src/main/java/org/gradoop/model/impl/operators/SummarizationCross.java]
> 3 [Implementation using joins|https://github.com/dbs-leipzig/gradoop/blob/%2345_gradoop_flink/gradoop-flink/src/main/java/org/gradoop/model/impl/operators/SummarizationJoin.java]
> 4 [Tests|https://github.com/dbs-leipzig/gradoop/blob/%2345_gradoop_flink/gradoop-flink/src/test/java/org/gradoop/model/impl/EPGraphSummarizeTest.java]
> 5 [TestGraph|https://github.com/dbs-leipzig/gradoop/blob/%2345_gradoop_flink/dev-support/social-network.pdf]
> I would basically use the same implementation as in 3 in combination with KeySelectors
to select the grouping keys on vertices and edges.
> As you can see in the example, each vertex in the resulting graph has a vertex id that
is contained in the original graph. This id is the smallest id among the grouped vertices
(e.g., vertices 2, 3 and 4 represent Dresden, so 2 is the group representative). The latter
is necessary to correctly assign the summarized edges. Maybe there is a smarter way to do
it of which I did not think of yet.
> I would like to contribute this to Flink and of course, if you have any suggestions/improvements
or do not want this at all (hopefully not), please let me know.



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