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Transitive Closure in Pig

1. Introduction

This a follow-up on my previous post about implementing PageRank in Pig using embedding. I also talked about this in a presentation to the Pig user group.
One of the best features of embedding is how it simplifies writing UDFs and using them right away in the same script without superfluous declarations. Computing a transitive closure is a good example of an algorithm requiring an iteration, a few simple UDFs and an end condition to decide when to stop iterating. Embedding is available in Pig 0.9. Knowledge of both Pig and Python is required to follow. Examples are available on github.

2. The problem

Before diving into the solution I will give a brief overview of the problem. We want to find the connected components of a graph by performing a transitive closure. Of course I will assume that the graph does not fit in main memory otherwise what follows is not very useful.
A picture is worth a thousand words; here is a visual statement of the problem:

Transitive Closure

Transitive Closure

I highlighted the diameter in red as it plays an important role in the complexity of the algorithm. The diameter of a connected component is the longest shortest path between 2 nodes of the component.
The algorithm will require log2(max(diameter of a component)) iterations because every iteration we double the number of relations that have been followed. This is not the overall complexity but it ensures that the number of iterations will stay low as with just 10 iterations you can handle components with a diameter of 1000+. In most real life use cases the diameter is very low and a few iterations will suffice.

3. The algorithm

I wrote the following implementation to illustrate the embedding feature. It may not be optimal but it is a working solution with a reasonable number of iterations. The algorithm does a graph traversal from all the nodes in parallel. It does one hop per iteration (pardon the scientific jargon) and then merges the results per node (using follow() and OR()). As a consequence the diameter of the graph followed from a node doubles every iteration. In this case, the edges of the graph are considered bidirectional and are stored one way (see normalize() and bidirectional()) to save space. The edges are stored in two files: followed (empty at the beginning) and to_follow which will tell us when all the edges have been followed (to_follow is empty). The last part of the script does some formatting to turn a list of edges into group of nodes (using sort() to make sure they are always represented the same way).

4. The code

Here is an example of how to solve this problem by embedding Pig in Python.
(explanation follows)
Input data (data/tc_data_simple.txt):

id0	id1
id1	id2
id2	id3
id3	id4
id4	id5
id5	id6
id6	id7
id7	id8
id11	id10
id12	id11
id13	id12
id14	id13
id14	id15
id15	id16
id16	id17
id17	id18



from org.apache.pig.scripting import *

@outputSchema("rels:{t:(id1: chararray, id2: chararray)}")
def bidirectional(id1, id2):
    if id2 != id1:
        return [ (id1, id2), (id2, id1) ]
        return [ (id1, id2) ]

def normalize(t):
    id1, id2, followed = t;
    if id2>id1:
        return (id1, id2, followed)
        return (id2, id1, followed)

@outputSchema("rels:{t:(id1: chararray, id2: chararray, followed: int)}")
def follow(to_follow_id1, links_id1, links_id2):
    outputBag = [ normalize( (links_id1, links_id2, True) ) ]
    if to_follow_id1 is not None:
        outputBag.append( normalize( (to_follow_id1, links_id2, False) ) )
    return outputBag

@outputSchema("followed: int")
def OR(bag):
    result = False;
    for followed in bag:
        result = result | followed[0]
    return result  

@outputSchema("group: {t: (id: chararray)}")
def SORT(bag):
    return bag

def main():
    # cleanup output directory before starting
    Pig.fs("rmr out/tc")
    Q = Pig.compile("""
    followed = LOAD ‘$followed’ AS (id1: chararray, id2: chararray);
    followed = FOREACH followed GENERATE FLATTEN(bidirectional(id1, id2)), 1 AS followed; — 1 == true
    to_follow = LOAD ‘$to_follow’ AS (id1: chararray, id2: chararray);
    to_follow = FOREACH to_follow GENERATE FLATTEN(bidirectional(id1, id2)), 0 AS followed; — 0 == false
    links = UNION to_follow, followed;
    joined_links = JOIN links BY id1 LEFT, to_follow BY id2;
    new_links_dup =
        FOREACH joined_links
        GENERATE FLATTEN( follow(to_follow::rels::id1, links::rels::id1, links::rels::id2) );

    new_links =
        FOREACH (GROUP new_links_dup BY (id1, id2))
        GENERATE group.id1, group.id2, OR(new_links_dup.followed);

    SPLIT new_links INTO new_followed IF followed != 0, new_to_follow IF followed == 0;
    new_followed = FOREACH new_followed GENERATE id1, id2;
    new_to_follow = FOREACH new_to_follow GENERATE id1, id2;
    STORE new_followed INTO ‘$new_followed’;
    STORE new_to_follow INTO ‘$new_to_follow’;
    to_follow = "data/tc_data_simple"
    followed = "out/tc/followed_0"
    # create empty dataset for first iteration
    Pig.fs("mkdir " + followed)
    Pig.fs("touchz " + followed + "/part-m-00000")
    for i in range(10):
        new_to_follow = "out/tc/to_follow_" + str(i + 1)
        new_followed = "out/tc/followed_" + str(i + 1)
        job = Q.bind().runSingle()
        if not job.isSuccessful():
            raise ‘failed’
        to_follow = new_to_follow
        followed = new_followed
        # detect if we are done
        if not job.result("new_to_follow").iterator().hasNext():

    links = LOAD ‘$followed’ AS (id1: chararray, id2: chararray);
    links = FOREACH links GENERATE FLATTEN( bidirectional(id1, id2) );
    result = DISTINCT (
        FOREACH (GROUP links by id1)
        GENERATE SORT(links.id2));
    STORE result INTO ‘out/tc/groups’;

if __name__ == ‘__main__’:

Output data:


5. Notables

There are a few things to notice in this implementation:
– UDFs are just defined by functions in the same script
– The output schema of the UDF is defined by using the @outputSchema decorator. Pig needs the schema of the output to interpret the statements following the UDF call.
– The native Python structures (dictionary, tuple, list) are used, the conversion to Pig types (Map, tuple, bag) is automatic. This makes the UDF code much more compact.
– UDFs are directly available in embedded Pig scripts using the function names. No other declaration is required.
– We iterate a maximum of 10 times (max diameter = 210 = 1024) and check if the “to follow” relation is empty to decide if we need to stop the iteration. This is done using the JobStats object returned by runSingle().

There’s also an experimental Javascript embedding that I’ll talk about in a future post.


6 responses to “Transitive Closure in Pig

  1. Antonio Piccolboni August 23, 2011 at 11:39 am

    I may be missing some detail, but it looks like your algorithm is a map reduce implementation of the PRAM algorithm “random mate”, which has already been ported to mapreduce in R and RHIPE by yours truly (http://blog.piccolboni.info/2011/04/map-reduce-algorithm-for-connected.html) a few months ago.

    • julienledem August 23, 2011 at 2:08 pm

      Hi Antonio,
      Thank you for your comment, it is always interesting when people come up with similar ideas independently. The algorithm I present is limited by the diameter (and size) of components as I looked into this to implement dedupplication in a context where components where small.
      I’ll make sure to read your blog in details!

      If you are interested in history, this particular implementation is a simplification of the version I had presented at the summer hack day 2009 at Yahoo! to illustrate Pig embedding which eventually made its way into open source merged with similar contributions from other people (PIG-928, PIG-1479). The code is available as pyg.tgz attached to the JIRA: https://issues.apache.org/jira/browse/PIG-928

  2. Vijayakumar Ramdoss August 27, 2011 at 11:20 am

    Its interesting and well explained one.

  3. rabidgremlin February 21, 2012 at 7:25 pm

    Hi there,

    I’m getting the following errors when trying to run this example:

    org.apache.pig.backend.executionengine.ExecException: ERROR 0: Error executing function
    at org.apache.pig.scripting.jython.JythonFunction.exec(JythonFunction.java:106)
    at org.apache.pig.backend.hadoop.executionengine.physicalLayer.expressionOperators.POUserFunc.getNext(POUserFunc.java:216)
    at org.apache.pig.backend.hadoop.executionengine.physicalLayer.expressionOperators.POUserFunc.getNext(POUserFunc.java:258)
    at org.apache.pig.backend.hadoop.executionengine.physicalLayer.PhysicalOperator.getNext(PhysicalOperator.java:316)
    at org.apache.pig.backend.hadoop.executionengine.physicalLayer.relationalOperators.POForEach.processPlan(POForEach.java:332)

    at org.apache.pig.backend.hadoop.executionengine.physicalLayer.relationalOperators.POForEach.getNext(POForEach.java:284)
    at org.apache.pig.backend.hadoop.executionengine.physicalLayer.PhysicalOperator.processInput(PhysicalOperator.java:290)
    at org.apache.pig.backend.hadoop.executionengine.physicalLayer.relationalOperators.POSplit.getNext(POSplit.java:214)
    at org.apache.pig.backend.hadoop.executionengine.mapReduceLayer.PigMapBase.runPipeline(PigMapBase.java:261)
    at org.apache.pig.backend.hadoop.executionengine.mapReduceLayer.PigMapBase.map(PigMapBase.java:256)
    at org.apache.pig.backend.hadoop.executionengine.mapReduceLayer.PigMapBase.map(PigMapBase.java:58)
    at org.apache.hadoop.mapreduce.Mapper.run(Mapper.java:144)
    at org.apache.hadoop.mapred.MapTask.runNewMapper(MapTask.java:621)
    at org.apache.hadoop.mapred.MapTask.run(MapTask.java:305)
    at org.apache.hadoop.mapred.LocalJobRunner$Job.run(LocalJobRunner.java:177)
    Caused by: Traceback (most recent call last):
    File “tc.py”, line 26, in generateRelationshipsForTC
    id1, attrs1 = subject
    TypeError: ‘NoneType’ object is not iterable

    I’m using pig 9.0 and Jython 2.5.2. Any ideas as too what is going wrong? Thanks

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