UF.scala

object UnionFind {
  def undirectedEdge(tuple: (String, String)) = tuple :: tuple.swap :: Nil
  def findRepresentative(it: Iterator[(String, String)]) = {
    val (existingRepr, newReprCandidate) = it.next()
    val newRepr = if(existingRepr.compareTo(newReprCandidate) <= 0) existingRepr else newReprCandidate
    val updated = it.nonEmpty && (existingRepr != newRepr)
    val items = (Iterator(existingRepr, newReprCandidate) ++ it.map(_._2)).filter(_ != newRepr)
    items.map(k => (newRepr, k, updated))
  }

  def unionFindStep(stat: Stat, pairs: TypedPipe[(String, String)]) = {
    val result = formNewRepresentatives(pairs)
      .map{t3 =>
        if(t3._3) stat.inc
        t3
      }
      .debug
      .map(t3 => (t3._1, t3._2))
      .distinct
      .forceToDiskExecution
    result
  }

  def unionFind(pairs: TypedPipe[(String, String)]) = {
    val key = StatKey("new-representatives", "unionfind")

    def execute(stat: Stat, pairs: TypedPipe[(String, String)], iteration: Int): Execution[(Int, TypedPipe[(String, String)])] = {
      println(s"Running iteration $iteration")
      unionFindStep(stat, pairs)
        .getAndResetCounters
        .flatMap{
          case (newPairs, counters) =>
            println(s"Completed iteration $iteration, # newUpdates: ${counters(key)}")
            val newUpdatesAvailable = counters(key)
            if (newUpdatesAvailable == 0L) Execution.from(iteration, newPairs)
            else execute(stat, newPairs, iteration+1)
        }
    }

    Execution.withId{ implicit uid =>
      execute(Stat(key), pairs, 1)
    }
  }

  def formNewRepresentatives(pairs: TypedPipe[(String,String)]) = {
    pairs
      .flatMap(undirectedEdge)
      .groupBy(_._1).sortBy(_._2)
      .mapValueStream(values => findRepresentative(values))
      .values
  }

}

Some logs for posterity...

Running iteration 1
SLF4J: Failed to load class "org.slf4j.impl.StaticLoggerBinder".
SLF4J: Defaulting to no-operation (NOP) logger implementation
SLF4J: See http://www.slf4j.org/codes.html#StaticLoggerBinder for further details.
['(aaa,bbb,false)']
['(aaa,ccc,false)']
['(aaa,ddd,false)']
['(aaa,bbb,false)']
['(aaa,ccc,false)']
['(aaa,ddd,true)']
['(aaa,eee,true)']
['(ddd,eee,true)']
['(ddd,fff,true)']
['(ddd,yyy,true)']
['(eee,fff,false)']
['(eee,yyy,false)']
tuples count: 12
Completed iteration 1, # newUpdates: 5
Running iteration 2
['(aaa,bbb,false)']
['(aaa,ccc,false)']
['(aaa,ddd,false)']
['(aaa,eee,false)']
['(aaa,bbb,false)']
['(aaa,ccc,false)']
['(aaa,ddd,true)']
['(aaa,eee,true)']
['(aaa,fff,true)']
['(aaa,yyy,true)']
['(aaa,eee,true)']
['(aaa,ddd,true)']
['(aaa,fff,true)']
['(aaa,yyy,true)']
['(ddd,fff,true)']
['(ddd,eee,true)']
['(ddd,yyy,true)']
['(ddd,eee,true)']
tuples count: 18
Completed iteration 2, # newUpdates: 0

If you look at the above logs, all records that has "true" in the 3rd field are expected to increment the counter, which it does in the actual unionFindStep function. But, when I try to use them in the execute function inside unionFind, inside the flatMap, counters doesn't even have that key,group. All this observation holds true, after 2nd iteration completes.

Updated working code:

def unionFindStep(stat: Stat, pairs: TypedPipe[(String, String)]) = {
    val result = formNewRepresentatives(pairs)
      .map{t3 =>
        if(t3._3) stat.inc
        t3
      }
      .forceToDiskExecution

    val hasUpdates = result.flatMap{ pipe =>
      pipe
        .filter(_._3)
        .map(_ => 1L)
        .sum[Long]
        .toOptionExecution
        .map(_.getOrElse(0L))
    }

    val distinctPairs = result.map(pipe => pipe.map(t3 => (t3._1, t3._2)).distinct)
    Execution.zip(hasUpdates, distinctPairs)
  }

  def unionFind(pairs: TypedPipe[(String, String)]) = {
    val key = StatKey("new-representatives", "unionfind")

    def execute(stat: Stat, pairs: TypedPipe[(String, String)], iteration: Int): Execution[(Int, TypedPipe[(String, String)])] = {
      println(s"Running iteration $iteration")
      unionFindStep(stat, pairs)
        .getAndResetCounters
        .flatMap{
          case ((hasUpdates, newPairs), counters) =>
            println(s"Completed iteration $iteration, # newUpdates: ${hasUpdates}")
            if (hasUpdates == 0L) Execution.from(iteration, newPairs)
            else execute(stat, newPairs, iteration+1)
        }
    }

    Execution.withId{ implicit uid =>
      execute(Stat(key), pairs, 1)
    }
  }