Optimal simulations by Butterfly Networks
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Simulating Binary Trees on Hypercubes
AWOC '88 Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures
Embedding an Arbitrary Binary Tree into the Star Graph
IEEE Transactions on Computers
Optimal Parallel Routing in Star Networks
IEEE Transactions on Computers
Embedding Torus on the Star Graph
IEEE Transactions on Parallel and Distributed Systems
Longest Fault-Free Paths in Star Graphs with Edge Faults
IEEE Transactions on Computers
Embedding Binary Trees into Crossed Cubes
IEEE Transactions on Computers
Embedding Star Networks into Hypercubes
IEEE Transactions on Computers
Embeddings into the pancake interconnection network
HPC-ASIA '97 Proceedings of the High-Performance Computing on the Information Superhighway, HPC-Asia '97
Comparing star and pancake networks
The essence of computation
Hyper hamiltonian laceability on edge fault star graph
Information Sciences: an International Journal
Embedding longest fault-free paths onto star graphs with more vertex faults
Theoretical Computer Science
Conditional fault-tolerant hamiltonicity of star graphs
Parallel Computing
Fault-free longest paths in star networks with conditional link faults
Theoretical Computer Science
Optimal fault-tolerant Hamiltonicity of star graphs with conditional edge faults
The Journal of Supercomputing
Edge-bipancyclicity of star graphs with faulty elements
Theoretical Computer Science
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Simulations of hypercube networks by certain Cayley graphs on the symmetric group are investigated. Let Q(k) be the familiar k-dimensional hypercube, and let S(n) be the star network of dimension n defined as follows. The vertices of S(n) are the elements of the symmetric group of degree n, two vertices x and y being adjacent if xo(1,i)=y for some i. That is, xy is an edge if x and y are related by a transposition involving some fixed symbol (which we take to be /spl I.bold/1). This network has nice symmetry properties, and its degree and diameter are sublogarithmic as functions of the number of vertices, making it compare favorably with the hypercube network. These advantages of S(n) motivate the study of how well it can simulate other parallel computation networks, in particular, the hypercube. The first step in such a simulation is the construction of a one-to-one map f:Q(k)/spl rarr/S(n) of dilation d, for d small. That is, one wants a map f such that images of adjacent points are at most distance d apart in S(n). An alternative approach, best applicable when one-to-one maps are difficult or impossible to find, is the construction of a one-to-many map g of dilation d, defined as follows. For each point x/spl isin/Q(k), there is an associated subset g(x)/spl sube/V(S(n)) such that for each edge xy in Q(k), every x'/spl isin/g(x) is at most distance d in S(n) from some y'/spl isin/g(y). Such one-to-many maps allow one to achieve the low interprocessor communication time desired in the usual one-to-one embedding underlying a simulation. This is done by capturing the local structure of Q(k) inside of S(n) (via the one-to-many embedding) when the global structure cannot be so captured. Our results are the following. 1) There exist the following one-to-many embeddings: a) f:Q(k)/spl rarr/S(3k+1) with dilation (f)=1; b) f:Q(11k+2)/spl rarr/S(13k+2) with dilation (f)=2. 2) There exists a one-to-one embedding f:Q(n2/sup n/spl minus/1/)/spl rarr/S(2/sup n/) with dilation (f)=3.