Assigns edges to partitions by hashing the source and destination vertex IDs in a canonical direction, resulting in a random vertex cut that colocates all edges between two vertices, regardless of direction.
Assigns edges to partitions using only the source vertex ID, colocating edges with the same source.
Assigns edges to partitions using a 2D partitioning of the sparse edge adjacency matrix,
guaranteeing a 2 * sqrt(numParts)
bound on vertex replication.
Assigns edges to partitions using a 2D partitioning of the sparse edge adjacency matrix,
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:
__________________________________ v0 | P0 * | P1 | P2 * | v1 | **** | * | | v2 | ******* | ** | **** | v3 | ***** | * * | * | ---------------------------------- v4 | P3 * | P4 *** | P5 ** * | v5 | * * | * | | v6 | * | ** | **** | v7 | * * * | * * | * | ---------------------------------- v8 | P6 * | P7 * | P8 * *| v9 | * | * * | | v10 | * | ** | * * | v11 | * <-E | *** | ** | ----------------------------------
The edge denoted by E
connects v11
with v1
and is assigned to processor P6
. To get the
processor number we divide the matrix into sqrt(numParts)
by sqrt(numParts)
blocks. Notice
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)
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.
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.
Assigns edges to partitions by hashing the source and destination vertex IDs, resulting in a random vertex cut that colocates all same-direction edges between two vertices.
Returns the PartitionStrategy with the specified name.
Collection of built-in PartitionStrategy implementations.