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1.  final def !=(arg0: Any): Boolean

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2.  final def ##(): Int

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3.  final def ==(arg0: Any): Boolean

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4.  final def asInstanceOf[T0]: T0

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5.  def clone(): AnyRef

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6.  final def eq(arg0: AnyRef): Boolean

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7.  def equals(arg0: Any): Boolean

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8.  def finalize(): Unit

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9.  def fromString(s: String): PartitionStrategy

   Returns the PartitionStrategy with the specified name.

10.  final def getClass(): Class[_]

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11.  def hashCode(): Int

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12.  final def isInstanceOf[T0]: Boolean

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13.  final def ne(arg0: AnyRef): Boolean

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14.  final def notify(): Unit

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15.  final def notifyAll(): Unit

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16.  final def synchronized[T0](arg0: ⇒ T0): T0

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17.  def toString(): String

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18.  final def wait(): Unit

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19.  final def wait(arg0: Long, arg1: Int): Unit

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20.  final def wait(arg0: Long): Unit

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21.  object CanonicalRandomVertexCut extends PartitionStrategy with Product with Serializable

    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.

22.  object EdgePartition1D extends PartitionStrategy with Product with Serializable

    Assigns edges to partitions using only the source vertex ID, colocating edges with the same source.

23.  object EdgePartition2D extends PartitionStrategy with Product with Serializable

    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.

24.  object RandomVertexCut extends PartitionStrategy with Product with Serializable

    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.