How to implement cycle detection with pyspark graphframe pregel API

Question

I am trying to implement the algorithm from Rocha & Thatte (http://cdsid.org.br/sbpo2015/wp-content/uploads/2015/08/142825.pdf) with Pyspark and the pregel wraper from graphframes. Here I am getting stuck with the correct syntax for the message aggregation.

The idea is strait forward:

...In each pass, each active vertex of G sends a set of sequences of vertices to its out- neighbours as described next. In the first pass, each vertex v sends the message (v) to all its out- neighbours. In subsequent iterations, each active vertex v appends v to each sequence it received in the previous iteration. It then sends all the updated sequences to its out-neighbours. If v has not received any message in the previous iteration, then v deactivates itself. The algorithm terminates when all the vertices have been deactivated. ...

My idea is to send the vertices ids to the destination vertices (dst) and in the aggregation function collect them into a list. Then in my vertex column "sequence" I would like to append/merge this new list items with the existing one and then do a check with when statements if the current vertex id is already in the sequence. Then I could set the vertex according vertex columns to true to flag them as in a cycle. But I can't find the correct syntax in Spark on how to concatenate this. Does anyone has an idea? Or implemented something similar?

My current code

from pyspark import SparkContext, SparkConf
from pyspark.sql import SparkSession
from pyspark.sql import SQLContext
import pyspark.sql.functions as f
from pyspark.sql.functions import coalesce, col, lit, sum, when

from graphframes import GraphFrame
from graphframes.lib import *



SimpleCycle=[
    ("1","2"),
    ("2","3"),
    ("3","4"),
    ("4","5"),
    ("5","2"),
    ("5","6")
]


edges = sqlContext.createDataFrame(SimpleCycle,["src","dst"]) \
    .withColumn("self_loop",when(col("src")==col("dst"),True).otherwise(False))
edges.show()

+---+---+---------+
|src|dst|self_loop|
+---+---+---------+
|  1|  2|    false|
|  2|  3|    false|
|  3|  4|    false|
|  4|  5|    false|
|  5|  2|    false|
|  5|  6|    false|
+---+---+---------+

vertices=edges.select("src").union(edges.select("dst")).distinct().distinct().withColumnRenamed('src', 'id') 
#vertices = spark.createDataFrame([[1], [2], [3], [4],[5],[6],[7],[8],[9]], ["id"])


#vertices.sort("id").show()

graph = GraphFrame(vertices, edges)

cycles=graph.pregel \
    .setMaxIter(5) \
    .withVertexColumn("is_cycle", lit(""),lit("logic to be added")) \
    .withVertexColumn("sequence", lit(""),Pregel.msg()) \
    .sendMsgToDst(Pregel.src("id")) \
    .aggMsgs(f.collect_list(Pregel.msg())) \
    .run()

cycles.show()

+---+-----------------+--------+
| id|         is_cycle|sequence|
+---+-----------------+--------+
|  3|logic to be added|     [2]|
|  5|logic to be added|     [4]|
|  6|logic to be added|     [5]|
|  1|logic to be added|    null|
|  4|logic to be added|     [3]|
|  2|logic to be added|  [5, 1]|
+---+-----------------+--------+

Code that does not work but what I think the logic should be

cycles=graph.pregel \
    .setMaxIter(5) \
    .withVertexColumn("is_cycle", lit(""), \ 
        when(Pregel.src("id").isin(Pregel.src(sequence)),True).otherwise(False) \
    .withVertexColumn("sequence", lit("null"),Append_To_Existing_List(Pregel.msg()) \
    .sendMsgToDst(
        when(Pregel.src("sequence").isNull(),Pregel.src("id")) \ 
        .otherwise(Pregel.src("sequence")) \
    .aggMsgs(f.collect_list(Pregel.msg())) \
    .run()

# I would like to have a result like
+---+-----------------+---------+
| id|         is_cycle|sequence |
+---+-----------------+---------+
|  1|false            |     [1] |
|  2|true             |[2,3,4,5]|
|  3|true             |[2,3,4,5]|
|  4|true             |[2,3,4,5]|
|  5|true             |[2,3,4,5]|
|  6|false            |  null   |
+---+-----------------+---------+

Answer 1

Finally I implemented Rocha-Thatte algorithm not via pregel but with the underlying message aggregation function of graphframe/graphX. In case someone is interested I'd like to share the solution

This solution works correctly and can handle very large graphs without failing However it is getting quite slow if the cycle length or the graph is long. Not sure how to improve this right now. Possibly in using checkpoints or broadcasting in a smart way

Happy about any input for improvement

# spark modules
from pyspark import SparkContext, SparkConf
from pyspark.sql import SparkSession
from pyspark.sql import SQLContext
from pyspark.sql.types import *
from pyspark.sql import Row
from pyspark.sql.window import Window
import pyspark.sql.functions as f

# graphframes modules
from graphframes import GraphFrame
from graphframes.lib import *
AM=AggregateMessages


def find_cycles(sqlContext,sc,vertices,edges,max_iter=100000):

    # Cycle detection via message aggregation
    """
    This code is an implementation of the Rocha-Thatte algorithm for large-scale sparce graphs

    Source:
    ==============
    wiki:  https://en.wikipedia.org/wiki/Rocha%E2%80%93Thatte_cycle_detection_algorithm
    paper: https://www.researchgate.net/publication/283642998_Distributed_cycle_detection_in_large-scale_sparse_graphs

    The basic idea:
    ===============
    We propose a general algorithm for detecting cycles in a directed graph G by message passing among its vertices, 
    based on the bulk synchronous message passing abstraction. This is a vertex-centric approach in which the vertices 
    of the graph work together for detecting cycles. The bulk synchronous parallel model consists of a sequence of iterations, 
    in each of which a vertex can receive messages sent by other vertices in the previous iteration, and send messages to other 
    vertices.
    In each pass, each active vertex of G sends a set of sequences of vertices to its out- neighbours as described next. 
    In the first pass, each vertex v sends the message (v) to all its out- neighbours. In subsequent iterations, each active vertex v 
    appends v to each sequence it received in the previous iteration. It then sends all the updated sequences to its out-neighbours. 
    If v has not received any message in the previous iteration, then v deactivates itself. The algorithm terminates when all the 
    vertices have been deactivated.
    For a sequence (v1, v2, . . . , vk) received by vertex v, the appended sequence is not for- warded in two cases: (i) if v = v1, 
    then v has detected a cycle, which is reported (see line 9 of Algorithm 1); (ii) if v = vi for some i ∈ {2, 3, . . . , k}, 
    then v has detected a sequence that contains the cycle (v = vi, vi+1, . . . , vk, vk+1 = v); in this case, 
    the sequence is discarded, since the cycle must have been detected in an earlier iteration (see line 11 of Algorithm 1); 
    to be precise, this cycle must have been detected in iteration k − i + 1. Every cycle (v1, v2, . . . , vk, vk+1 = v1) 
    is detected by all vi,i = 1 to k in the same iteration; it is reported by the vertex min{v1,...,vk} (see line 9 of Algorithm 1).
    The total number of iterations of the algorithm is the number of vertices in the longest path in the graph, plus a few more steps 
    for deactivating the final vertices. During the analysis of the total number of iterations, we ignore the few extra iterations 
    needed for deactivating the final vertices and detecting the end of the computation, since it is O(1).
    
    Pseudocode of the algorithm:
    ============================
    M(v): Message received from vertex v
    N+(v): all dst verties from v

    functionCOMPUTE(M(v)):
        if i=0 then:
            for each w ∈ N+(v) do:
                send (v) to w 
        else if M(v) = ∅ then:
                deactivate v and halt 
        else:
            for each (v1,v2,...,vk) ∈ M(v) do:
                if v1 = v and min{v1,v2,...,vk} = v then:
                    report (v1 = v,v2,...,vk,vk+1 = v)
                else if v not ∈ {v2,...,vk} then:
                    for each w ∈ N+(v) do:
                        send (v1,v2,...,vk,v) to w

    
    Scalablitiy of the algorithm:
    ============================
    the number of iteration depends on the path of the longest cycle
    the scaling it between 
    O(log(n)) up to maxium O(n) where n=number of vertices
    so the number of iterations is less to max linear to the number of vertices, 
    if there are more edges (parallel etc.) it will not affect the the runtime


    for more details please refer to the oringinal publication
    """


    _logger.warning("+++ find_cycles(): starting cycle search ...")
    
    # create emtpy dataframe to collect all cycles
    cycles = sqlContext.createDataFrame(sc.emptyRDD(),StructType([StructField("cycle",ArrayType(StringType()),True)]))

    # initialize the messege column with own source id 
    init_vertices=(vertices
                   .withColumn("message",f.array(f.col("id")))
                  )
    
    init_edges=(edges
                .where(f.col("src")!=f.col("dst"))
                .select("src","dst")
                )
    
    # create graph object that will be update each iteration
    gx = GraphFrame(init_vertices, init_edges)

    # iterate until max_iter 
    # max iter is used in case that the3 break condition is never reached during this time
    # defaul value=100.000
    for iter_ in range(max_iter):
        
        # message that should be send to destination for aggregation
        msgToDst = AM.src["message"]
        # aggregate all messages that where received into a python set (drops duplicate edges)
        agg = gx.aggregateMessages(
            f.collect_set(AM.msg).alias("aggMess"),
            sendToSrc=None,
            sendToDst=msgToDst)
        
        # BREAK condition: if no more messages are received all cycles where found 
        # and we can quit the loop        
        if(len(agg.take(1))==0):
            #print("THE END: All cycles found in " + str(iter_) + " iterations")
            break
        
        # apply the alorithm logic 
        # filter for cycles that should be reported as found
        # compose new message to be send for next iteration
        # _column name stands for temporary columns that are only used in the algo and then dropped again
        checkVerties=(
            agg
            # flatten the aggregated message from [[2]] to [] in order to have proper 1D arrays
            .withColumn("_flatten1",f.explode(f.col("aggMess")))
            # take first element of the array
            .withColumn("_first_element_agg",f.element_at(f.col("_flatten1"), 1))
            # take minimum element of th array
            .withColumn("_min_agg",f.array_min(f.col("_flatten1")))
            # check if it is a cycle 
            # it is cycle when v1 = v and min{v1,v2,...,vk} = v
            .withColumn("_is_cycle",f.when(
                (f.col("id")==f.col("_first_element_agg")) &
                (f.col("id")==f.col("_min_agg"))
                 ,True)
                .otherwise(False)
            )
            # pick cycle that should be reported=append to cylce list
            .withColumn("_cycle_to_report",f.when(f.col("_is_cycle")==True,f.col("_flatten1")).otherwise(None))
            # sort array to have duplicates the same
            .withColumn("_cycle_to_report",f.sort_array("_cycle_to_report"))
            # create column where first array is removed to check if the current vertices is part of v=(v2,...vk)
            .withColumn("_slice",f.array_except(f.col("_flatten1"), f.array(f.element_at(f.col("_flatten1"), 1)))) 
            # check if vertices is part of the slice and set True/False column
            .withColumn("_is_cycle2",f.lit(f.size(f.array_except(f.array(f.col("id")), f.col("_slice"))) == 0))
           )
        
        #print("checked Vertices")
        #checkVerties.show(truncate=False)
        # append found cycles to result dataframe via union
        cycles=(
            # take existing cycles dataframe
            cycles
            .union(
                # union=append all cyles that are in the current reporting column
                checkVerties
                .where(f.col("_cycle_to_report").isNotNull())
                .select("_cycle_to_report")
                )
        )

        # create list of new messages that will be send in the next iteration to the vertices
        newVertices=(
            checkVerties
            # append current vertex id on position 1
            .withColumn("message",f.concat(
                f.coalesce(f.col("_flatten1"), f.array()),
                f.coalesce(f.array(f.col("id")), f.array())
            ))
            # only send where it is no cycle duplicate
            .where(f.col("_is_cycle2")==False)
            .select("id","message")
        )

        print("vertics to send forward")
        newVertices.sort("id").show(truncate=False)
        
        # cache new vertices using workaround for SPARK-1334
        cachedNewVertices = AM.getCachedDataFrame(newVertices)

        # update graphframe object for next round
        gx = GraphFrame(cachedNewVertices, gx.edges)


    
    # materialize results and get number of found cycles
    #cycles_count=cycles.persist().count()

    _cycle_statistics=(
        cycles
        .withColumn("cycle_length",f.size(f.col("cycle")))
        .agg(f.count(f.col("cycle")),f.max(f.col("cycle_length")),f.min(f.col("cycle_length")))
        ).collect()

    cycle_statistics={"count":_cycle_statistics[0]["count(cycle)"],"max":_cycle_statistics[0]["max(cycle_length)"],"min":_cycle_statistics[0]["min(cycle_length)"]}
    
    end_time =time.time()
    _logger.warning("+++ find_cycles(): " + str(cycle_statistics["count"]) + " cycles found in " + str(iter_) + " iterations (min length=" + str(cycle_statistics["min"]) +", max length="+ str(cycle_statistics["max"]) +") in " + str(end_time-start_time) + " seconds")
    _logger.warning("+++ #########################################################################################")


    return cycles, cycle_statistics

this functions takes a graphs like

SimpleCycle:

NestedCycle:

SimpleCycle=[
    ("0","1"),
    ("1","2"),
    ("2","3"),
    ("3","4"),
    ("3","1")]

NestedCycle=[
    ("1","2"),
    ("2","3"),
    ("3","4"),
    ("4","1"),
    ("3","1"),
    ("5","1"),
    ("5","2")]

edges = sqlContext.createDataFrame(SimpleCycle,["src","dst"])

vertices=edges.select("src").union(edges.select("dst")).distinct().distinct().withColumnRenamed('src', 'id') 

edges.show()
# +---+---+
# |src|dst|
# +---+---+
# |  1|  2|
# |  2|  3|
# |  3|  4|
# |  4|  1|
# |  3|  1|
# |  5|  1|
# |  5|  2|
# +---+---+


raw_cycles=find_cycles(sqlContext,sc,vertices,edges,max_iter=1000)

raw_cycles.show()
# +------------+
# |       cycle|
# +------------+
# |   [1, 2, 3]|
# |[1, 2, 3, 4]|
#+------------+