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[SPARK-8718] [GRAPHX] Improve EdgePartition2D for non perfect square number of partitions

Browse source 
See https://github.com/aray/e2d/blob/master/EdgePartition2D.ipynb

Author: Andrew Ray <ray.andrew@gmail.com>

Closes #7104 from aray/edge-partition-2d-improvement and squashes the following commits:

3729f84 [Andrew Ray] correct bounds and remove unneeded comments
97f8464 [Andrew Ray] change less
5141ab4 [Andrew Ray] Merge branch 'master' into edge-partition-2d-improvement
925fd2c [Andrew Ray] use new interface for partitioning
001bfd0 [Andrew Ray] Refactor PartitionStrategy so that we can return a prtition function for a given number of parts. To keep compatibility we define default methods that translate between the two implementation options. Made EdgePartition2D use old strategy when we have a perfect square and implement new interface.
5d42105 [Andrew Ray] % -> /
3560084 [Andrew Ray] Merge branch 'master' into edge-partition-2d-improvement
f006364 [Andrew Ray] remove unneeded comments
cfa2c5e [Andrew Ray] Modifications to EdgePartition2D so that it works for non perfect squares.
This commit is contained in:
Andrew Ray 2015-07-14 13:14:47 -07:00 committed by Ankur Dave
parent d267c2834a
commit 0a4071eab3
1 changed files with 21 additions and 11 deletions
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32
graphx/src/main/scala/org/apache/spark/graphx/PartitionStrategy.scala
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@ -32,7 +32,7 @@ trait PartitionStrategy extends Serializable {
object PartitionStrategy {
/**
* Assigns edges to partitions using a 2D partitioning of the sparse edge adjacency matrix,
* guaranteeing a `2 * sqrt(numParts) - 1` bound on vertex replication.
* guaranteeing a `2 * sqrt(numParts)` bound on vertex replication.
*
* Suppose we have a graph with 12 vertices that we want to partition
* over 9 machines. We can use the following sparse matrix representation:
@ -61,26 +61,36 @@ object PartitionStrategy {
* that edges adjacent to `v11` can only be in the first column of blocks `(P0, P3,
* P6)` or the last
* row of blocks `(P6, P7, P8)`. As a consequence we can guarantee that `v11` will need to be
* replicated to at most `2 * sqrt(numParts) - 1` machines.
* replicated to at most `2 * sqrt(numParts)` machines.
*
* Notice that `P0` has many edges and as a consequence this partitioning would lead to poor work
* balance. To improve balance we first multiply each vertex id by a large prime to shuffle the
* vertex locations.
*
* One of the limitations of this approach is that the number of machines must either be a
* perfect square. We partially address this limitation by computing the machine assignment to
* the next
* largest perfect square and then mapping back down to the actual number of machines.
* Unfortunately, this can also lead to work imbalance and so it is suggested that a perfect
* square is used.
* When the number of partitions requested is not a perfect square we use a slightly different
* method where the last column can have a different number of rows than the others while still
* maintaining the same size per block.
*/
case object EdgePartition2D extends PartitionStrategy {
override def getPartition(src: VertexId, dst: VertexId, numParts: PartitionID): PartitionID = {
val ceilSqrtNumParts: PartitionID = math.ceil(math.sqrt(numParts)).toInt
val mixingPrime: VertexId = 1125899906842597L
val col: PartitionID = (math.abs(src * mixingPrime) % ceilSqrtNumParts).toInt
val row: PartitionID = (math.abs(dst * mixingPrime) % ceilSqrtNumParts).toInt
(col * ceilSqrtNumParts + row) % numParts
if (numParts == ceilSqrtNumParts * ceilSqrtNumParts) {
// Use old method for perfect squared to ensure we get same results
val col: PartitionID = (math.abs(src * mixingPrime) % ceilSqrtNumParts).toInt
val row: PartitionID = (math.abs(dst * mixingPrime) % ceilSqrtNumParts).toInt
(col * ceilSqrtNumParts + row) % numParts
} else {
// Otherwise use new method
val cols = ceilSqrtNumParts
val rows = (numParts + cols - 1) / cols
val lastColRows = numParts - rows * (cols - 1)
val col = (math.abs(src * mixingPrime) % numParts / rows).toInt
val row = (math.abs(dst * mixingPrime) % (if (col < cols - 1) rows else lastColRows)).toInt
col * rows + row
}
}
}