Load balancing
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Load-Balancing. Load-Balancing. What is load-balancing? Dividing up the total work between processes when running codes on a parallel machine Load-balancing constraints Minimize interprocess communication Also called: partitioning, mesh partitioning, (domain decomposition).

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Load-Balancing

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Load balancing

Load-Balancing

High Performance Computing 1


Load balancing1

Load-Balancing

  • What is load-balancing?

    • Dividing up the total work between processes when running codes on a parallel machine

  • Load-balancing constraints

    • Minimize interprocess communication

  • Also called:

    • partitioning, mesh partitioning, (domain decomposition)

High Performance Computing 1


Know your data and memory

Know your data and memory

  • Memory is organized by banks. Between access to any bank, there is a latency period.

  • Matrix entries are stored column-wise in FORTRAN.

High Performance Computing 1


Load balancing

Matrix addressing in FORTRAN

is addressed

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Addressing memory

Addressing Memory

  • For illustration purposes, lets imagine 8 banks [128 or 256 common on chips today], with bank busy time (bbt) of 8 cycles between accesses. Thus we have:

    data a13 a23 a33 a43 a14 a24 a34 a44

    data a11 a21 a31 a41 a12 a22 a32 a42

    bank 1 2 3 4 5 6 7 8

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Addressing memory1

Addressing Memory

  • If we access data column-wise, we proceed through each bank in order. By the time we call a13, we (just) avoid bbt.

  • On the other hand, if we access data row-wise, we get a11 in bank 1, a12 in bank 5, a13 in bank 1 again - so instead of access on clock cycle 3, we have to wait until cycle 9. Then we get a14 in bank 5 again on cycle 10, etc.

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Indirect addressing

Indirect addressing

  • If addressing is indirect we may wind up jumping all over, and suffer performance hits because of it.

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Shared memory

Shared Memory

  • Bank conflicts depend on granularity of memory

  • If N memory refs per cycle, p processors, memory with b cycles bbt, need p*N*b memory banks to see uninterrupted access of data

  • With B banks, granularity is

    g = B/(p*N*b)

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Moral

Moral

  • Separate selection of data from its processing

  • Each subtask requires its own data structure. Be prepared to change structures between tasks

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Load balancing nomenclature

Load-balancing nomenclature

Objects get distributed among different processes

Edges represent information that need to be shared between objects

Object

Edge

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Partitioning

Partitioning

  • Divides up the work

    • 5 & 4 objects assigned to processes

  • Creates “edge-cuts”

    • Necessary communications between processes

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Work edge weights

Work/Edge Weights

  • Need a good measure of what the expected work may be

    • Molecular dynamics:

      • number of molecules

      • regions

    • FEM/finite difference/finite volume, etc:

      • Degrees of freedom

      • Cells/elements

  • If edge weights are used, also need a good measure on how strongly objects are coupled to each other

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Static dynamic load balancing

Static/Dynamic Load-Balancing

  • Static load-balancing

    • Done as a “preprocessing” step before the actual calculation

    • If the objects and edges don’t change very much or at all, can do static load-balancing

  • Dynamic load-balancing

    • Done during the calculation

    • Significant changes in the objects and/or edges

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Dynamic load balancing example

Dynamic Load-Balancing Example

  • h-adapted mesh

  • Workload is changing as the computation proceeds

  • Calculate a new partition

  • Need to migrate the elements to their assigned process

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Static vs dynamic load balancing

Static vs. Dynamic Load Balancing

  • Static partitioning insufficient for many applications

    • Adaptive mesh refinement

    • Multi-phase/Multi-physics computations

    • Particle simulations

    • Crash simulations

    • Parallel mesh generation

    • Heterogeneous computers

  • Need dynamic load balancing

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Dynamic load balancing constraints

Dynamic Load-Balancing Constraints

  • Minimize load-balancing time

    • Memory constraints

  • Minimize data migration -- incremental partitions

    • Small changes in the computation should result in small changes in the partitioning

    • Calculating new partition and data migration should take less time than the amount of time saved by performing computations on new grid

  • Done in parallel

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Methods of load balancing

Methods of Load-Balancing

  • Geometric

    • Based on geometric location

    • Faster load-balancing time with medium quality results

  • Graph-based

    • Create a graph to represent the objects and their connections

    • Slower load-balancing time but high quality results

  • Incremental methods

    • Use graph representation and “shuffle” around objects

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Choosing a load balancing algorithm method

Choosing a Load-Balancing Algorithm/Method

No algorithm/method is appropriate for all applications!

  • Graph load-balancing algorithms for:

    • Static load-balancing

    • Computations where computation to load-balancing time ratio is high

      • Implicit schemes with a linear and non-linear solution scheme

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Choosing a load balancing algorithm method1

Choosing a Load-Balancing Algorithm/Method

  • Geometric load-balancing algorithms for:

    • Computations where computation to load-balancing time ratio is low

      • For explicit time stepping calculations with many time steps and varying workload (MD, FEM crash simulations, etc.)

      • Problems with many load-balancing objects

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Geometric load balancing

Geometric Load-Balancing

  • Based on the objects’ coordinates

    • Want a unique coordinate associated with an object

      • Node coordinates, element centroid, molecule coordinate/centroid, etc.

  • Partition “space” which results in a partition of the load-balancing objects

  • Edge cuts are usually not explicitly dealt with

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Geometric load balancing assumptions

Geometric Load-Balancing Assumptions

  • Objects that are close will likely need to share information

    • Want compact partitions

      • High volume to surface area or high area to perimeter length ratios

  • Coordinate information

  • Bounded domain

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Geometric load balancing algorithms

Geometric Load-Balancing Algorithms

  • Recursive Coordinate Bisection (RCB)

    • Berger & Bokhari

  • Recursive Inertial Bisection (RIB)

    • Taylor & Nour-Omid

  • Space Filling Curves (SFC)

    • Warren & Salmon, Ou, Ranka, & Fox, Baden & Pilkington

  • Octree Partitioning/Refinement-tree Partitioning

    • Loy & Flaherty, Mitchell

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Recursive coordinate bisection

Recursive Coordinate Bisection

  • Choose an axis for the cut

  • Find the proper location of the cut

  • Group objects together according to location relative to cut

  • If more partitions are needed, go to step 1

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Recursive inertial bisection

Recursive Inertial Bisection

  • Choose a direction for the cut

  • Find the proper location of the cut

  • Group objects together according to location relative to cut

  • If more partitions are needed, go to step 1

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Space filling curves

Space Filling Curves

A Space Filling Curve is a 1-dimensional curve which passes through every point in an n-dimensional domain

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Load balancing with space filling curves

Load-Balancing with Space Filling Curves

  • The SFC gives a 1-dimensional ordering of objects located in an n-dimensional domain

    • Easier to work with objects in 1 dimension than in n dimensions

  • Algorithm:

    • Sort objects by their location on the SFC

    • Calculate cuts along the SFC

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Octree partitioning refinement tree partitioning

Tree based algorithms for applications with multiple levels of data, simulation accuracy, etc.

Tree is usually built from specific computational schemes

Tightly coupled with the simulation

Octree Partitioning/Refinement-Tree Partitioning

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Comparisons of rcb rib and sfc

Comparisons of RCB, RIB, and SFC

  • RCB and RIB usually give slightly better partitions than SFC

  • SFC is usually a little faster

  • SFC is a little better for incremental partitions

    • RIB can be real unstable for incremental partitions

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Load balancing libraries

Load-Balancing Libraries

  • There are many load-balancing libraries downloadable from the web

    • Mostly graph partitioning libraries

      • Static: Chaco, Metis, Party, Scotch

      • Dynamic: ParMetis, DRAMA, Jostle, Zoltan

  • Zoltan (www.cs.sandia.gov/Zoltan)

    • Dynamic load-balancing library with:

      • SFC, RCB, RIB, Octree, ParMetis, Jostle

    • Same interface to all load-balancing algorithms

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Methods to avoid communication

Methods to Avoid Communication

  • Avoiding load-balancing

    • Load-balancing not needed every time the workload and/or edge connectivity changes

  • Ghost cells

  • Predictive load-balancing

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Accessing information on other processors

Accessing Information on Other Processors

  • Need communication between processors

  • Use ‘ghost’ cells – need to maintain consistency of data in ghost cells

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Ghost cells

Ghost Cells

  • Copies of cells assigned to other processors

  • Make needed information available

  • No solution values are computed at the ghost cells

  • Ghost cell information needs to be updated whenever necessary

  • Ghost cells need to be calculated dynamically because of changing mesh and dynamic load-balancing

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Predictive load balancing

Predictive Load-Balancing

  • Predict the workload and/or edge connectivity and load-balance with that information

    • Assumes that you can predict the workload and/or edge connectivity

  • Still need to perform communication but reduces data migration

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Predictive load balancing1

Predictive Load-Balancing

  • Refine then load-balance – 4 objects migrated

  • Predictive load-balance then refine – 1 object migrated

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