Communications of the ACM - Special section on computer architecture
Designing efficient algorithms for parallel computers
Designing efficient algorithms for parallel computers
Topological Properties of Hypercubes
IEEE Transactions on Computers
Minimal Mesh Embeddings in Binary Hypercubes
IEEE Transactions on Computers
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
High-performance computer architecture (2nd ed.)
High-performance computer architecture (2nd ed.)
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Computer Architecture and Parallel Processing
Computer Architecture and Parallel Processing
Interconnection Networks for Parallel and Distributed Processing
Interconnection Networks for Parallel and Distributed Processing
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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Due to its attractive topological properties, the hypercube multiprocessor has emerged as one of the architectures of choice when it comes to implementing a large number of computational problems. In many such applications, Gray-code labelings of the hypercube are a crucial prerequisite for obtaining efficient algorithms. We propose a greedy algorithm that, given an n-dimensional hypercube H with N=2n nodes, returns a Gray-code labeling of H , that is, a labeling of the nodes with binary strings of length n such that two nodes are neighbors in the hypercube if, and only if, their labels differ in exactly one bit. Our algorithm is conceptually very simple and runs in O(Nlog N) time being, therefore, optimal. As it turns out, with a few modifications our labeling algorithm can be used to recognize hypercubes as well.