Parallel Processing: Best Data Partitioning Strategies for Maximum Efficiency

In parallel processing, data is divided among multiple processing units. They either share memory or communicate over a network. This depends on the architecture. Each processor works on a designated part of the data, either independently or through coordinated task scheduling. In many cases, the computed results are aggregated at the end to produce the final output.

A key factor in efficient parallel execution is how data is partitioned, as it directly affects performance and load distribution. In this blog, I will explore three fundamental data partitioning strategies: Block Partitioning, Cyclic Partitioning, and Block-Cyclic Partitioning. This discussion will focus specifically on how these techniques work in parallel computing.

Before diving into partitioning strategies, let’s start with a simple dataset:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

For this discussion, we’ll assume we have three symmetric processors—P0, P1, and P2. While processors don’t necessarily have to be symmetric in real-world scenarios, we’re making this assumption here to keep things simple.

Our goal is to partition or divide the dataset into different segments and assign them to each processor. Nonetheless, what each processor does with the data is beyond the scope of this blog. Instead, we’ll focus solely on the partitioning strategies in the next sections.

Block partitioning

In block partitioning, the dataset is divided into smaller, contiguous blocks. The exact criteria for division vary. Nonetheless, the core idea remains the same: split the data into equal-sized subsets. Then assign each subset to a processor.

For this discussion, we have three processors. We can divide the dataset into three equal partitions. Each partition holds four data elements. Each partition is then assigned to its respective processor.

A possible block diagram representation of this partitioning method is shown below:

Figure 1: Block Partitioning Strategy

The diagram illustrates block partitioning. A dataset of 12 elements (0–11) is evenly divided into three contiguous blocks. Each block is assigned to a separate processor (P0, P1, P2).

• Processor P0 receives the first four elements: {0, 1, 2, 3}
• Processor P1 handles the next block: {4, 5, 6, 7}
• Processor P2 processes the last four elements: {8, 9, 10, 11}

This method ensures a balanced workload when data is evenly divisible. It is an efficient strategy for parallel computing. This approach results in minimal communication overhead between processors.

Cyclic Partitioning Strategy

In the cyclic partitioning strategy, data elements are assigned to processors in a round-robin fashion. Each processor receives one element at a time in sequential order. After the last processor is assigned an element, the assignment cycle restarts from the first processor. This process continues until all elements in the dataset are distributed.

This approach ensures a more balanced workload when dealing with non-uniform or irregular data patterns. It prevents one processor from being overloaded while others stay idle.

A possible block diagram representation of cyclic partitioning is shown below:

Figure 2: Cyclic Partitioning Strategy

The diagram above illustrates the cyclic partitioning strategy, where data elements are assigned to processors using a round-robin approach. Unlike block partitioning, where contiguous chunks of data are assigned, cyclic partitioning distributes elements in a rotational manner across processors.

Here’s how it works:

• Round 0: The first three elements (0, 1, 2) are assigned to P0, P1, and P2, respectively.
• Round 1: The next three elements (3, 4, 5) continue the cycle, assigned again to P0, P1, and P2.
• Round 2 & 3: The cycle repeats until all elements are distributed.

At the end of the process:

• P0 handles {0, 3, 6, 9}
• P1 handles {1, 4, 7, 10}
• P2 handles {2, 5, 8, 11}

This method ensures better load balancing, especially in scenarios where certain computations take longer for specific data points. By evenly distributing the workload, cyclic partitioning prevents some processors from becoming idle. Others stay overloaded. This makes it a useful strategy in parallel computing environments.

The next approach combines the strengths of block partitioning and cyclic partitioning to achieve utmost efficiency. As the name suggests, this method is called the Block-Cyclic Partitioning Strategy—a fusion of both techniques.

In the next section, we’ll explore how this strategy works and why it is useful in parallel computing.

Block Cyclic Partitioning Strategy

In the Block-Cyclic Partitioning Strategy, data is first divided into smaller blocks. These blocks are then assigned to processors in a round-robin fashion. This approach blends the principles of block partitioning and cyclic partitioning to improve workload distribution.

Let’s take the same dataset used earlier and divide it into smaller sets:

{0, 1}, {2, 3}, {4, 5}, {6, 7}, {8, 9}, {10, 11}

Now, we don’t assign individual elements one by one. Instead, we group elements together as in cyclic partitioning. We assign each smaller group to processors in rounds. This method is like the round-robin approach.

Since data is initially divided using the Block Partitioning method, it retains its block structure. Nonetheless, the assignment process follows the Cyclic Partitioning rule, ensuring an even distribution among processors. This hybrid strategy provides better load balancing and efficient parallel execution, which is why it is called Block-Cyclic Partitioning.

The next diagram visually shows how this partitioning strategy works.

Figure 3: Block-Cyclic Partitioning Strategy

Step 1: Breaking the Dataset into Smaller Blocks

As shown in the diagram, the original dataset {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} is first divided into smaller blocks of size 2:

• {0,1}, {2,3}, {4,5}, {6,7}, {8,9}, {10,11}

This block division follows the Block Partitioning principle, ensuring that each smaller group consists of consecutive elements from the dataset.

Step 2: Cyclic Assignment to Processors

Now that we have smaller data blocks, the next step is to assign these blocks to processors. We will use a round-robin policy. This policy is characteristic of Cyclic Partitioning.

Round 0:

• P0 receives {0,1}
• P1 receives {2,3}
• P2 receives {4,5}

Since all processors have received one block each, Round 0 ends here.

Round 1:

Following the same cyclic pattern:

• P0 receives {6,7}
• P1 receives {8,9}
• P2 receives {10,11}

At the end of Round 1, the final distribution of data blocks across processors is:

• P0: {0,1} and {6,7}
• P1: {2,3} and {8,9}
• P2: {4,5} and {10,11}

This hybrid approach ensures better load balancing compared to pure block partitioning. It still leverages the locality benefits of assigning contiguous chunks of data. This is why Block-Cyclic Partitioning is widely used in parallel computing and high-performance applications.

Now that we understand the three major data partitioning strategies, we will explore their implementation. They are implemented programmatically using MPI (Message Passing Interface) for parallel execution.

Stay tuned for the next section, where we’ll dive into real-world implementation. Till then, happy learning!