Hypercube Sort in C++

Hypercube Sort is a parallel sorting algorithm that can efficiently sort massive amounts of data over several processors. Its basis is the hypercube architecture, where each processor and node is viewed as a vertex inside an n-dimensional hypercube. The main concept is to carry out exchanges and comparisons using the hypercube's structure in a way that minimizes overall communication costs and evenly distributes the sorting workload. Using a looping process based on the binary encoding of each node's (processor's) index, the approach sorts data in a hypercube. The nodes communicate with their neighbors at every stage to swap elements and sort data concurrently.

Key Concepts of Hypercube Sort:

Several concepts of the Hypercube Sort in C++ are as follows:

• Hypercube Topology: A hypercube of dimension n contains 2^n nodes. If the difference between any two nodes' addresses each of which is an n-bit binary number is exactly one bit, then the nodes are connected.
• Parallel Processing: In the interaction between the processors, the hypercube shape helps greatly because they now have to share the dataset, which is divided among them. The neighbors of each processor are responsible for sorting the data portions that they own and communicating with their immediate neighbors to create a globally sorted array.
• Recursive Sorting: The method reduces the initial problem by breaking it down into various little sub-problems and dealing with them parallelly, which fits the processors' way of working.

Basic Steps Followed in Hypersort Cube:

• Distribution of Data: The data is first partitioned and distributed across the nodes of the hypercube.
• Dimension-wise Sorting: At each stage of this algorithm, the hypercube is sorted according to one particular dimension. For instance, considering one of the dimensions, each node along that dimension will compare and swap data with its neighbor so that data will be moved closer to where it should be placed.
• Recursive halving: Use the form of the hypercube by recursively halving the amount of data that needs to be sorted at each step.
• Final Merge: When all dimensions have been sorted recursively, the sorted data is integrated across all nodes.

Consideration for Implementation Using C++:

• Parallel Libraries: During the implementation of a hypercube sort in C++, parallel libraries like MPI (Message Passing Interface) could be used to manage connections among processors.
• Distributed Data Structures: Because the data is partitioned across many CPUs, sorting and collection of local data entails some amount of work.
• Efficiency: For large-scale parallel processing systems, hypercube sort will be very effective due to the balanced workload it maintains with minimized processor communication.

Example:

Step 1:

Install MPI Library:

UBUNTU COMMANDS:

Step 2: Compile using MPI Compiler:

Step 3: Command For Running MPI Compiler:

Code:

Output:

 
Rank 0: 1 2 
Rank 1: 3 4 
Rank 2: 5 6 
Rank 3: 7 8   

Conclusion:

In the Hypercube Sort, the sorting work is distributed among several processors with low communication costs and utmost efficiency in sorting. Hypercube Sort breaks up the data and scatters its parts among close nodes following their binary addresses. From this, large datasets can be parallelly sorted by Hypercube into an efficient parallel sorting technique that drastically reduces the time it takes to perform a sort in distributed systems. MPI is used in Hypercube Sort's C++ version to show how tasks can work together to achieve global sorting despite local sorting and inter-process communication. This makes the algorithm highly competitive when it comes to high-performance computing, which is necessary for massive parallelism to be an effective sorting method in distributed memory systems.