PDP Chapter 5: Basic communication operations

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Questions and Answers

What is the primary goal of the One-to-All Broadcast operation?

To send a message from one processor to all other processors. (correct)

To efficiently route data to the target processor only.

To perform a computation specifically on multiple data inputs.

To combine messages from multiple processors into one.

In the context of All-to-One Reduction, what is the result of the operation?

The maximum value from all processors.

A single value computed from multiple inputs. (correct)

A list of values gathered from all processors.

The average of values from all processors.

When using recursive doubling for the One-to-All Broadcast, what is being optimized?

The time taken to transfer messages to all destination processors.

The total number of processors involved in the operation.

The number of messages sent from the source processor. (correct)

The network bandwidth used during the process.

In a Scatter operation, what is accomplished?

Data from one source is divided and sent to multiple destinations. Signup and view all the answers

What does the All-reduce process achieve?

It combines data across all processors and distributes the combined result to each processor. Signup and view all the answers

During the Gather operation, what is the role of the destination processor?

To combine data received from all source processors into a single output. Signup and view all the answers

What is one common misconception about the All-to-All Reduction operation?

It does not require any form of communication between processors. Signup and view all the answers

Which operation utilizes both the One-to-All Broadcast and All-to-One Reduction methods for data handling?

All-reduce process. Signup and view all the answers

What is the primary function of the All-Reduce process?

Combining the results of several nodes using an operator Signup and view all the answers

In a scatter operation, what happens at the node that initiates the process?

It sends a unique message to every other node. Signup and view all the answers

How does the gather operation function in distributed processing?

It allows a single node to collect messages from all nodes. Signup and view all the answers

Which of the following best describes All-to-All broadcast?

Each node broadcasts the same message to every other node. Signup and view all the answers

What is a potential application of All-to-All reduction?

Aggregating data from every node for a comprehensive result. Signup and view all the answers

When performing an All-Reduce operation, which operation might be used?

Combining results using Min, Max, Sum, or logical operations. Signup and view all the answers

In the context of parallel processing, what is the goal of the gather operation?

To combine multiple messages into one message. Signup and view all the answers

Which of the following statements about the All-to-One reduction is true?

It sends all nodes' data to a single node for aggregation. Signup and view all the answers

What is the primary purpose of a one-to-all broadcast in matrix-vector multiplication?

To distribute the vector element to all corresponding column processors. Signup and view all the answers

How does the all-to-one reduction operation function in the context of matrix-vector multiplication?

It sums the local products and sends them to the first row. Signup and view all the answers

In a square mesh, what is the mechanism for performing broadcast and reduction operations across rows and columns?

A row-wise operation is followed by a column-wise operation. Signup and view all the answers

What characteristic of a hypercube allows for the generalization of mesh algorithms?

It comprises multiple dimensions, each with two nodes. Signup and view all the answers

What is the main advantage of using scatter operations in parallel processing?

It allows one processor to send data to multiple processors simultaneously. Signup and view all the answers

What is primarily involved in the all-reduce process within a distributed system?

Processors execute a local operation and then perform a reduction simultaneously. Signup and view all the answers

What distinguishes the gather operation from other communication types in parallel processing?

It involves collecting data from various processors to a single destination. Signup and view all the answers

Which scenario exemplifies the all-to-all reduction process?

Collecting and distributing results among all processors to ensure each has the final result. Signup and view all the answers

Study Notes

One-to-All Broadcast and All-to-One Reduction

Processors are connected and can communicate
Data can be combined using operations like addition, minimum, maximum, AND, OR, or XOR
One-to-all broadcast: Single processor sends data to all other processors
All-to-one reduction: Data from all processors is combined and sent to a single processor
Example: One processor has a vector, and another processor has a matrix. The vector can be broadcast to rows of processors, and the rows can calculate the product of the vector and matrix. This can be done concurrently for all rows. Then, the results can be summed using all-to-one reduction along the columns of processors.

Recursive Doubling for One-to-All and All-to-One

Efficient way to perform one-to-all broadcast and all-to-one reduction on a ring of processors
How it works:
- Source processor initially broadcasts the data to another processor
- Now, two independent problems are created, each with half the number of processors
- The same procedure of broadcasting and reduction can be performed on the two halves
- This process is repeated until all processors have the data (for broadcast) or the result is available at the desired processor (for reduction)
Example: On an 8-node ring:
- Source processor (Node 0) sends data to Node 1 in the first step
- Node 0 and Node 1 both send data to Node 2 and Node 3 in the second step
- This continues until all nodes have the data

All-Reduce

Combines one-to-all broadcast and all-to-one reduction
How it works:
- All-to-one reduction is first performed to combine data from every processor to a single processor
- Then, the combined data is broadcast to all processors using one-to-all broadcast
Example: Given data A0 to F0 on different processors, the all-reduce operation would combine the data into H0 (A0 * B0 * C0 * D0 * E0 * F0) and then broadcast H0 to all of the processors.

Scatter and Gather

Scatter operation: A single node sends a unique message to every other node
Gather operation: A single node collects a unique message from each node

Broadcast and Reduction on a Mesh

A grid of p processors with √p processors in each row and column can be viewed as a 2D array.
How it works:
- Broadcast or reduction is first performed along each row, followed by concurrent operations along each column
- This can be generalized to higher dimensions
Example: Broadcasting a message on a 16-node (4x4) mesh:
- In the first step, the message is broadcast along the first row
- In the second step, the message is broadcast along each of the four columns

Broadcast and Reduction on a Hypercube

A hypercube with 2d nodes can be viewed as a d-dimensional mesh with two nodes in each dimension.
How it works :
- The mesh algorithm can be generalized to a hypercube, with operations carried out in d (= log p) steps
Example: Broadcasting on a 3-dimensional hypercube:
- In the first step, a node broadcasts the data to the other node in its dimension
- This is repeated in the other two dimensions

Matrix-Vector Multiplication Example

How broadcast and reduction can be used to efficiently multiply a matrix with a vector on a distributed system
Each row of a processor grid is assigned a row of the matrix
The first row is assigned the vector
Broadcast the vector to all processors in a column
Concurrently perform the local product of the vector and the matrix row
Finally, use all-to-one reduction to sum the local products within each column, resulting in the final vector output
This computation can be done concurrently for all columns of the matrix.

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Description

This quiz explores the concepts of one-to-all broadcast and all-to-one reduction in parallel processing. It delves into the operations used for data combination, such as addition and logical operations, and discusses efficient methods like recursive doubling for communication among processors. Test your understanding of these important parallel processing techniques.