Sorting networks and their applications

Question

1. What are the contributions in this paper?

2. What are other applications of sorting memories?

3. What is the simplest way to sort a bitonic sequence?

4. How many bits can be placed between different levels?

Accepted Answer

This paper describes networks that have a fast sorting or ordering capability ( sorting networks or sorting memories ).

Accepted Answer

Other applications of sorting memories are as a switching network with bu ering, a multiaccess memory, a multiaccess content-addressable memory and as a multiprocessor.

Accepted Answer

Since any two monotonic sequences can be put together to form a bitonic sequence a network which rearranges a bitonic sequence into monotonic order (a bitonic sorter) can be used as a merging network.

Accepted Answer

Parallel-input-parallel-output registers of 1024 bits each can be placed between certain levels to perform this task or the re-clocking may be incorporated within each comparison element with a pair of ipops on the outputs.

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Multi-processorBy adding processing logic to perform additions, subtractions, etc., on groups of adjacent words of a sorting memory one can implement a multi-processor.

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The adjacent word transfer sends back signals over each path to signal each input and output line whether or not a connection has been established.

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Doubling the size of a merge only increases the longest path by unity so the merging time increases slowly with the size of the network.

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It has the advantages over a normal crossbar of requiring less hardware (an n-input n-output switching network can be built with approximately ( 14 )n(log2n) 2 elements versus n2 in a normal crossbar) and of having a constant fan-in and a fan-out requirement on its elements.

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Multi-access content addressable memoryBy adding facilities for shifting the bits within the words in the aforementioned memory di erent elds of the words can be brought into the more-signi cant positions which govern the ordering of the words.

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While a complete cycle may be long in this memory (50-bit words at 100 nanoseconds/bit = 5 microseconds/recirculation = 10 microseconds/complete cycle) many inputs and outputs can be accommodated in each cycle.

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A major problem in the design of such a computing system is the connecting together of the various parts of the system (the I/O devices, memories, processing units, etc.) in such a way that all the required data transfers can be accommodated.

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Each input line inserts a word containing the output address desired (or zeroes if the line is inactive), a control bit equal to 1 and a priority number into an m-item sorting network with bi-directional elements.

Accepted Answer

An \\s by t" merging network can be built by presenting the odd-indexed numbers of the two input lists to one small merging network (the odd merge), presenting the even-indexed number to another small merging network (the even merge) and then comparing the outputs of these small merges with a row of comparison elements.

Accepted Answer

Such fast sorting capability can be used to manipulate large sets of data quickly and solve some of the communications problems associated with large-scale computing systems.

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The s + t outputs of the merging network present the s+t numbers of the merged lists in ascending order, c2; c2; :::; cs+t.A \\1 by 1" merging network is simply one comparison element.

Accepted Answer

Each path goes through ( 1 2 )p(p+ 1) levels.8 numbers4-number bitonic sortersA sorter of 1024 numbers will have 55 levels and 24,063 elements with odd-even merges or 28,160 elements with bitonic sorters.

Sorting networks and their applications

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Most frequently asked questions

1. What are the contributions in this paper?

2. What are other applications of sorting memories?

3. What is the simplest way to sort a bitonic sequence?

4. How many bits can be placed between different levels?

5. What is the function of a multi-processor?

6. What is the function of the adjacent word transfer?

7. What is the effect of doubling the size of a merge?

8. What is the advantage of a sorting network over a normal crossbar?

9. What is the function of the multi-access content addressable memory?

10. How many inputs and outputs can be accommodated in a complete cycle?

11. What is the problem in the design of a computing system?

12. What is the function of the m-item sorting network?

13. What is the simplest way to build a s by t" merging network?

14. What is the use of fast sorting capability?

15. What is the s+t output of the merging network?

16. How many elements are needed to sort a number?

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Citations

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References

On the Synthesis of Signal Switching Networks with Transient Blocking

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