Improving parallel efficiency

Understanding Parallel Efficiency

Parallel efficiency measures how effectively additional resources (cores, nodes, GPUs, etc.) are turned into extra performance.

Given speedup $S(p)$ on $p$ processing elements (PEs):

$$
\text{Parallel efficiency} \; E(p) = \frac{S(p)}{p}
$$

with $S(p)$ usually defined relative to a 1‑PE run or some baseline (e.g., 1 node, 1 GPU).

High efficiency ($E \approx 0.7 - 1$) means extra resources are well utilized; low efficiency means time and allocation are being wasted.

In practice you often look at:

• Strong-scaling efficiency: fixed problem size, more PEs.
• Weak-scaling efficiency: fixed work per PE, more PEs.

Improving parallel efficiency is about reducing everything that isn’t useful work: idle time, synchronization, overheads, and imbalance.

Anatomy of Parallel Overheads

To improve parallel efficiency, it helps to classify what reduces it:

1. Load imbalance
   Some PEs do more work than others, so fast PEs wait for slow ones.
2. Synchronization overheads
   Time spent at barriers, locks, critical regions, collective operations.
3. Communication overheads
   Time to send/receive data, including latency, bandwidth limitations, and contention.
4. Serial and poorly parallelized regions
   Code that runs on a single PE or with low concurrency.
5. Granularity and overhead of parallel constructs
   Too small tasks or too many parallel regions cause scheduling/management overhead.
6. Memory and data locality effects
   Cache misses, NUMA penalties, remote memory access, and contention can make parallel work slower.
7. Algorithmic mismatch
   Using a parallel algorithm that scales poorly even if implementation is “perfect”.

Improving efficiency is about attacking these systematically.

Measuring and Locating Inefficiencies

You should not guess where inefficiency comes from. Use measurement:

• Timing decomposition
• Measure wall-time of whole run.
• Split into phases (I/O, compute, communication, setup, finalize).
• Within critical kernels, time key regions or loops.
• Per-PE timing
• Compare timings across ranks/threads (e.g., MPI rank 0–N).
• Look for outliers: slowest PE often determines total time.
• Profiling and tracing tools
• MPI time vs. compute time; time in collectives vs point-to-point.
• Thread idleness and time spent in OpenMP runtime.
• Hardware counters (cache misses, memory bandwidth, branch mispredictions).

Once you know where time is lost, you can apply targeted strategies.

Reducing Load Imbalance

Load imbalance directly hurts efficiency: the fastest PEs sit idle, waiting for the slowest.

Common Causes

• Data decomposition not matching variable computational cost (e.g., more work in some spatial regions, adaptive grids).
• Dynamic behavior (changing workload over time).
• Heterogeneous hardware performance (mixed CPU models, noisy neighbors).
• Serial or partially serial sections in a few PEs (e.g., I/O concentrated on rank 0).

Strategies to Improve Balance

Better Decomposition

• Domain decomposition with cost awareness
  Partition work using an estimate of cost (e.g., number of nonzeros in a matrix row, number of particles, cells, or interactions).
• Over-decomposition
• Split work into more tasks than PEs.
• Let a runtime (e.g., dynamic OpenMP scheduling, tasking, Charm++, Legion, etc.) assign tasks to PEs.
• This allows better balancing when cost per task varies.

Dynamic Scheduling (Shared Memory)

In OpenMP:

• Use schedule(dynamic) or schedule(guided) for variable-cost loops.
• Use tasks (#pragma omp task) for irregular or recursive workloads.
• Avoid extremely fine-grained tasks; combine with chunks to balance overhead vs. flexibility.

Dynamic Load Balancing (Distributed Memory)

• Use work stealing or explicit work redistribution:
• Some ranks request more work if they finish early.
• Redistribute data based on updated work estimates:
• E.g., periodically repartition a mesh or graph to match current load.
• Use libraries or partitioners (e.g., graph partitioners) that aim to equalize workload while minimizing communication.

Avoid Single-PE Bottlenecks

• Avoid doing heavy work on a single rank/thread:
• Use parallel I/O instead of one rank handling all I/O.
• Parallelize initialization/cleanup tasks.
• Use collective operations to distribute setup cost when possible.

Key idea: measure load per PE and adjust decomposition or scheduling until no PE is consistently “much slower” than others.

Reducing Synchronization and Contention

Synchronization is necessary but expensive when overused or poorly designed.

Barriers and Collective Synchronization

• Minimize barriers:
• Use them only when logical correctness requires global alignment.
• Replace global barriers with point-to-point or local synchronization where possible.
• Over-synchronization:
• Patterns like "barrier after every loop" or inside small time steps often kill efficiency.
• Analyze dependencies: if not all PEs depend on all others, use smaller groups or avoid explicit sync.

Locks and Critical Regions (Shared Memory)

• Reduce time spent in critical, atomic, and locks:
• Use private or thread-local accumulation followed by a parallel reduction.
• Replace critical updates with reduction clauses in OpenMP (reduction(+:sum) etc.).
• Use lock-free or more scalable data structures where available.
• Split global locks:
• Use per-bucket or per-object locks instead of one global lock.
• Avoid updating shared state in inner loops if it can be postponed.

Contention on Resources

• Avoid having many PEs writing to the same cache line or memory location:
• Apply padding to arrays of counters to avoid false sharing.
• Align data structures to cache line boundaries.
• Reduce contention on shared queues:
• Use distributed queues or work stealing rather than a single global queue.

Goal: ensure that PEs spend most of their time doing independent useful work, not waiting on others.

Reducing Communication Overhead

Communication is often the dominant cost at scale; reducing it is central to parallel efficiency.

Minimize Volume and Frequency

• Aggregate messages:
• Send fewer, larger messages instead of many tiny ones.
• Combine halo regions or multiple small updates into one buffer.
• Reduce redundant communication:
• Reuse data when possible instead of re-requesting.
• Cache results that will be reused by the same PE.

Overlap Communication with Computation

• Restructure algorithms to:
• Start communication early (nonblocking communication, asynchronous operations).
• Compute on local or already available data while waiting for remote data.
• Only wait when the communicated data is actually needed.

This can convert latency into hidden time, improving efficiency even if total communication volume is unchanged.

Improve Communication Patterns

• Use collective operations correctly:
• Replace manual trees or loops of sends/receives with optimized collectives when appropriate.
• Conversely, if a collective is overkill for a small subset of ranks, use point-to-point communication to reduce involvement.
• Localize communication:
• Map data so that most communication is among nearby ranks (in topology) to reduce hop count and contention.
• Use process mapping options of the scheduler or MPI runtime to align communication topology with the machine interconnect.

Reduce Synchronizing Collectives

• Avoid unnecessary global collectives in time-stepping loops:
• E.g., compute diagnostics less frequently.
• Batch global reductions (e.g., collect statistics every N steps, not every step).

Better communication design can substantially improve weak and strong scaling efficiency.

Improving Work Granularity and Parallel Structure

Too fine granularity leads to overhead from thread scheduling, task management, and kernel launches; too coarse granularity can create imbalance.

Choose Appropriate Task/Chunk Size

• Group small operations into larger tasks:
• Combine tiny loops or short kernels.
• Avoid creating tasks for trivial operations.
• Adjust scheduling chunks:
• Avoid schedule(dynamic,1) for expensive scheduling overhead if cost per iteration is uniform.
• Use larger chunk sizes or static scheduling when appropriate.

Reduce Parallel Region Overhead

• Minimize entering/leaving parallel regions repeatedly:
• Use a single outer parallel region and inner constructs (e.g., parallel around time loop, for inside).
• Combine parallel loops when they operate on the same data and have no dependence obstacles.

Avoid Nested Parallelism Overuse

• Nested parallel regions often oversubscribe cores and increase overhead.
• Prefer:
• A clear hierarchy: e.g., MPI between nodes, threads within nodes.
• Control of thread counts per level to avoid exceeding physical cores.

Objective: keep the cost of managing parallelism small relative to the cost of doing useful work.

Addressing Memory and Locality Issues in Parallel Context

Parallel efficiency is hurt if each PE spends its time waiting on memory instead of computing.

NUMA and Affinity

• Pin processes/threads to cores:
• Use appropriate binding/pinning options in your runtime or scheduler.
• Ensure local memory placement:
• Use “first touch” initialization so each thread touches the data it will use, causing it to be allocated in its local NUMA domain.
• Avoid frequent cross-socket memory accesses for main data structures.

Reduce Shared Resource Contention

• Balance memory bandwidth usage:
• Too many memory-bound threads on one socket can saturate bandwidth.
• Sometimes fewer threads per socket at higher per-thread performance yields better efficiency.
• Stagger heavy memory phases across PEs if possible, instead of all cores hitting memory simultaneously.

Data Layout for Parallel Access

• Use data layouts that encourage:
• Contiguous access patterns per PE.
• Minimal sharing of cache lines between PEs.
• Partition data structures to reduce cross-PE access.

While detailed cache and vectorization issues are handled elsewhere, here the focus is ensuring that the parallel structure doesn’t negate per-core optimizations.

Algorithmic Considerations for Efficiency

Even with perfect implementation, some algorithms inherently scale poorly.

Reduce Global Dependencies

• Limit use of global synchronization and global data:
• Prefer algorithms that use localized communication and partial information.
• Use hierarchical or multi-level algorithms:
• Cooperate within nodes first, then across nodes.
• Use multi-grid or domain decomposition methods that reduce long-range interactions.

Choose Algorithms with Better Parallel Scaling

• Prefer methods that allow:
• More independent tasks.
• Fewer global reductions and barriers.
• Less communication per unit of computation.

Sometimes achieving high efficiency requires changing the mathematical or algorithmic approach, not just tuning code.

Practical Workflow for Improving Parallel Efficiency

1. Establish a baseline
• Measure runtime and parallel efficiency at a few PE counts.
• Record per-phase and per-PE timings.
2. Identify dominant inefficiencies
• Use profiling to determine whether time is dominated by:
• Load imbalance
• Communication
• Synchronization
• Memory stalls
• Serial sections
3. Apply targeted changes
• If load imbalance dominates:
• Change data partitioning or scheduling; introduce over-decomposition or tasks.
• If communication dominates:
• Aggregate messages; change layout; reduce collective frequency; overlap with computation.
• If synchronization dominates:
• Remove unnecessary barriers; restructure reductions; reduce critical regions.
• If memory/locality dominates:
• Improve affinity and first-touch; adjust thread counts; partition data.
4. Re-measure and compare
• After each change, rerun at the same PE counts.
• Track efficiency improvements and ensure correctness.
5. Scale up gradually
• Once efficient at moderate scale, test larger PE counts.
• New bottlenecks may appear only at larger scales (e.g., collective latency, network contention).
6. Document findings
• Record which changes had the largest impact and under which conditions (problem size, PE count, architecture).

Rules of Thumb for High Parallel Efficiency

• Use enough work per PE: avoid running at very high PE counts for tiny problems.
• Avoid single-point bottlenecks: I/O, rank 0 logic, global locks.
• Balance work dynamically when cost is unpredictable.
• Reduce global synchronization and expensive collectives in inner loops.
• Overlap communication with computation when possible.
• Keep parallel constructs coarse-grained relative to computation.
• Consider algorithm changes if structural overheads dominate.

Sustained improvement in parallel efficiency comes from iterative measurement, targeted optimizations, and a willingness to adapt both implementation and algorithm as scale grows.