pyspark - 如何使用 pyspark graphframe pregel API 实现循环检测

Question

我正在尝试使用 Pyspark 和来自 graphframes 的预凝胶包装器实现来自 Rocha & Thatte ( http://cdsid.org.br/sbpo2015/wp-content/uploads/2015/08/142825.pdf ) 的算法。在这里，我遇到了消息聚合的正确语法问题。

这个想法是直截了当的:

...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. ...

我的想法是将顶点 ID 发送到目标顶点 (dst)，然后在聚合函数中将它们收集到一个列表中。然后在我的顶点列“序列”中，我想将这个新列表项与现有列表项附加/合并，然后检查 when 语句是否当前顶点 ID 已经在序列中。然后我可以根据顶点列将顶点设置为 true 以将它们标记为循环。但是我在 Spark 中找不到关于如何连接它的正确语法。有人有想法吗？或者实现了类似的东西？

我当前的代码

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]|
+---+-----------------+--------+

代码行不通但是我觉得逻辑应该是这样

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

最后我实现了 Rocha-Thatte 算法，不是通过预凝胶，而是通过底层graphframe/graphX的消息聚合功能。如果有人感兴趣，我想分享解决方案

这个解决方案工作正常，可以处理非常大的图而不会失败然而，如果周期长度或图表很长，它会变得很慢。现在不确定如何改进。可能以智能方式使用检查点或广播

对任何改进意见感到高兴

# 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

这个函数采用像这样的图形

简单循环:

嵌套循环:

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]|
#+------------+