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Fault Tolerance in Hypercubes [chapter]

Shobana Balakrishnan, Füsun Özgüner, Baback Izadi
1993 Parallel Computing on Distributed Memory Multiprocessors  
Therefore, a faulty hypercube needs to be reconfigured to perform both local and global communication as required by the algorithm, effectively and with minimal performance degradation.  ...  A study of hypercube algorithms reveals that in many cases, the computations that require local communication are mapped onto topologies such as meshes or rings and the hypercube topology is used for global  ...  Communication in Faulty Hypercubes Global Sum/Global Broadcast Algorithms for Healthy Hypercubes Efficient communication algorithms [30, 31] have been devised for healthy hypercubes.  ... 
doi:10.1007/978-3-642-58066-6_14 fatcat:3dbkhliutzeofgfnwzfqz7v2wy

Simulation of Meshes in a Faulty Supercube with Unbounded Expansion

JenChih Lin, ShihJung Wu
2011 International Journal of Advancements in Computing Technology  
We develop novel algorithms to facilitate the embedding job when the Incrementally Extensible Hypercube (IEH) contains faulty nodes.  ...  The paper considers the problem of finding meshes and tori in a Faulty Incrementally Extensible Hypercube if any.  ...  After a mesh is mapped in an IEH, we develop new algorithms to facilitate the embedding meshes and tori in a faulty IEH. Our results demonstrate that O(n 2 -⎣log 2 m ⎦ 2 ) faults can be tolerated.  ... 
doi:10.4156/ijact.vol3.issue8.33 fatcat:4whocads6zgyhmjutp3dyxi67u

The Hamiltonicity of Crossed Cubes in the Presence of Faults

Emad Abuelrub
2008 Engineering Letters  
Our result is optimal in the fact that it constructs the Hamiltonian circuit by avoiding only faulty nodes and edges in a crossed hypercube of dimension n.  ...  Our algorithm can tolerate up to 2 n-3 faults with the restriction that each sub cube CQ 3 has at most one faulty node.  ...  Many researchers have addressed the problem of embedding rings into hypercubes in the presence of faults.  ... 
dblp:journals/engl/Abuelrub08 fatcat:e2mlmqtqk5fdrednlvihhl4xb4

Page 8874 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
Therefore, this investi- gation presents a novel algorithm to facilitate the embedding job when the flexible hypercube contains faulty nodes.  ...  Although the embedding of complete binary trees in faulty hypercubes has received considerable attention, to our knowledge no paper has demonstrated how to embed a complete binary tree in a faulty flexible  ... 

Page 5632 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
These embedding algorithms show a complete binary tree can be embedded into a faulty flexible hypercube with load 1, congestion | and dilation 4 so that O(n?  ...  From the summary: “We develop novel algorithms to facilitate embedding when the flexible hypercube contains faulty nodes.  ... 

Distributed fault-tolerant ring embedding and reconfiguration in hypercubes

Yuh-Rong Leu, Sy-Yen Kuo
1999 IEEE transactions on computers  
In this paper, we propose a distributed ring-embedding algorithm that can find a Hamiltonian cycle in a fault-free or faulty n-dimensional hypercube (Q n ), and the complexity is O(n) parallel steps.  ...  Furthermore, a dynamic reconfiguration algorithm for an embedded ring is proposed and discussed.  ...  In [3] , centralized algorithms are devised for optimal ring embedding in an n-dimensional hypercube Q n with at most n − 2 faulty links.  ... 
doi:10.1109/12.743414 fatcat:rwm4tiislndbhmdoxomuako7jm

Reconfiguration of Complete Binary Trees in Full IEH Graphs and Faulty Hypercubes

Jen-Chih Lin, Huan-Chao Keh
2001 The international journal of high performance computing applications  
Moreover, the embedding algorithm can be also applied into hypercubes with one faulty node.  ...  As the model the authors proposed, an algorithm is developed for the embedding with expansion 1, load 1, congestion 2, and dilation 2.  ...  As a consequence, our embedding algorithm can be also applied to hypercubes with one faulty node.  ... 
doi:10.1177/109434200101500105 fatcat:jqxznv77jrgj7cjx3437ljrtsi

Embedding cube-connected cycles graphs into faulty hypercubes

J. Bruck, R. Cypher, D. Soroker
1994 IEEE transactions on computers  
We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with  ...  Our main result is an algorithm that, given a l i t of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges.  ...  ACKNOWLEDGMENT We would like to thank the anonymous referees for their helpful comments and suggestions.  ... 
doi:10.1109/12.324546 fatcat:nc6fz5qitjhbpcnbbmwo5hncvq

Page 5536 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with  ...  Our main result is an algorithm that, given a list of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges.  ... 

Page 3186 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
In order to reduce ex- ecution slowdown in a hypercube with given faults, it is essential to identify the maximum healthy subcubes in the faulty hypercube because the time for executing a parallel algorithm  ...  Our algorithm has a time complexity of O(mN) for fault-tolerant multicasting in a hypercube of N = 2” processors containing an arbitrary number of faulty processors.” 98e:68014 68MI10 68M15 90B25 Tamaki  ... 

Page 3442 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
Summary: “Embedding meshes in hypercubes has been studied extensively. Most earlier works on embedding in faulty hypercubes considered edge failures as node failures.  ...  A lower bound under the model is derived and efficient algorithms are developed to achieve broadcasting in O(n) communication time in a star graph S,, (with n!  ... 

Determining a Non-Collision Data Transfer Paths in Hypercube Processors Network [chapter]

Jan Chudzikiewicz, Zbigniew Zieliski
2012 Embedded Systems - High Performance Systems, Applications and Projects  
Processors in multiprocessor systems communicate with each other by sending messages. The problem of data transfer in hypercube systems has been widely analyzed in the literature.  ...  The implementation problem of the presented method in embedded systems has also been raised.  ...  Determining a Non-Collision Data Transfer Paths in Hypercube Processors Network, Embedded Systems -High Performance Systems, Applications and Projects, Dr.  ... 
doi:10.5772/38168 fatcat:5ywlnox24jfbvexxdx4twhteky

Cycles embedding in folded hypercubes with conditionally faulty vertices

Che-Nan Kuo, Yu-Huei Cheng
2017 Discrete Applied Mathematics  
When we want to design simple algorithms with low communication costs, cycles are suitable one.  ...  CYCLES EMBEDDING IN A FAULTY FOLDED HYPERCUBE Let ( ) represent the faulty vertex and/or faulty edge set which is incident to the end-vertices of any edge ∈ ( ).  ...  BIBE, FUZZ, iCAST, ICCI*CC, PEDS, TENCON, and VPPC to name just a few). In addition, he has also been actively  ... 
doi:10.1016/j.dam.2016.12.008 fatcat:27gjzwzcjjfnjdjkphu25oyqki

A generalized fault-tolerant sorting algorithm on a product network

Yuh-Shyan Chen, Chih-Yung Chang, Tsung-Hung Lin, Chun-Bo Kuo
2005 Journal of systems architecture  
Our generalized sorting algorithm can be applied to any product network only if the factor graph of the product graph can be embedding in a ring.  ...  This paper proposes a generalized algorithm for fault-tolerant parallel sorting in product networks.  ...  For example, a fault-tolerant sorting algorithm developed for a hypercube in [4] and [19] will not work on a grid, even though both hypercubes and grids are product networks.  ... 
doi:10.1016/j.sysarc.2004.11.005 fatcat:vy3q25ekbnggnga7lkwtt67ese

Fault-tolerant cycle embedding in dual-cube with node faults

Yamin Li, Shietung Peng, Wanming Chu
2005 International Journal of High Performance Computing and Networking  
In this paper, by using Gray code, we show that there exists a fault-free cycle containing at least 2 2m + 1 -2f nodes in DC(m), m ≥ 3, with f ≤ m faulty nodes.  ...  There are 2 m+1 clusters and hence the total number of nodes in a DC(m) is 2 2m + 1 .  ...  This feature is the key for designing efficient routing and communication algorithms in dual-cube.  ... 
doi:10.1504/ijhpcn.2005.007866 fatcat:27z5boxyljbdde5bsl56i576re
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