B. Aiello and T. Leighton, \Coding Theory, Hypercube Embedding and Fault Tolerance", Proceedings of 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, 1991, 125 - 136. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Distributed Computing On Anonymous Hypercubes With Faulty.. - Kranakis, Santoro (1992) (Correct)
....In this paper we give an algorithm for computing Boolean functions on asynchronous, anonymous hypercubes having bit complexity Here N is the number of nodes, n = log N . Since a connected, n dimensional hypercube with polylogarithmic number of faulty components has diameter O(log N) see [1]) we have an O(Npolylog(N) bit complexity for n dimensional hypercubes with 1 = polylog(N) faulty components. Notice the di erent estimates on the bit complexity implied by the algorithm for hypercubes with exactly one faulty link versus hypercubes with exactly one faulty processor; in the ....
....log log N ) In particular, the bit complexity stated in theorem 1 remains valid, even if the size of the input data is up to O( n ( bits. 2.3 Estimates depending on the number of faults Theorem 1 raises the problem of studying n ( as a function of . Results of B. Aiello and T. Leighton in [1] show that an n dimensional hypercube with worst case faults can simulate the fault free n dimensional hypercube Qn with only constant slowdown. In particular, this implies that n ( O(n) for = n . As a consequence we obtain the following result for hypercubes with polylogarithmic ....
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B. Aiello and T. Leighton, \Coding Theory, Hypercube Embedding and Fault Tolerance", Proceedings of 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, 1991, 125 - 136.
Deterministic Parallel Backtrack Search - Herley, Pietracaprina, Pucci (2001) (Correct)
.... and communication for the exploration of trees arising from irregular divide and conquer computations has been studied in [WK91] A number of related problems have also been addressed in the literature, such as branch and bound [Ran90,KZ93,LAB93,KP94,HPP99a,HPP99b] and dynamic tree embeddings [AL91,BGLL91,LNRS92]. In this paper, we present a deterministic PRAM algorithm for backtrack search whose running time is within a triply logarithmic factor of the natural lower bound discussed above. Our main result is summarized in the following theorem. Theorem 1 There is a deterministic algorithm running on a ....
B. Aiello and T. Leighton. Coding theory, hypercube embeddings and fault-tolerance. In Proceedings of 3rd ACM Symposium on Parallel Algorithms and Architectures, pages 125-136, 1991.
Fast Deterministic Backtrack Search - Herley, Pietracaprina, Pucci (1996) (Correct)
....been obtained previously for the completely connected network of processors [KZ93, LAB93] the butterfly network [Ran94] and the two dimensional mesh [KP94] under a variety of cost models. A number of related problems such as branch and bound [Ran90, KZ93, LAB93, KP94] and dynamic tree embedding [LNRS92, AL91, BGLL91] have also been addressed in the literature. Both Ranade s butterfly algorithm [Ran94] and the Karp Zhang algorithm [Ran90, KZ93] are randomized and explore the tree in O(n=p h) steps, with high probability. It should be noted that the butterfly algorithm focuses on the number of ....
B. Aiello and T. Leighton. Coding theory, hypercube embeddings and faulttolerance. In Proceedings of 3rd ACM Symposium on Parallel Algorithms and Architectures, pages 125--136, 1991.
Deterministic Parallel Backtrack Search - Herley, Pietracaprina, Pucci (2000) (Correct)
.... computation and communication for the exploration of trees arising from irregular divide and conquer computations has been studied in [WK91] A number of related problems have also been addressed in the literature, such as branch and bound [Ran90,KZ93,LAB93,KP94] and dynamic tree embeddings [AL91,BGLL91,LNRS92]. In this paper, we present a deterministic PRAM algorithm for backtrack search whose running time is within a triply logarithmic factor of the natural lower bound discussed above. Our main result is summarized in the following theorem. Theorem 1 There is a deterministic algorithm running on a ....
B. Aiello and T. Leighton. Coding theory, hypercube embeddings and fault-tolerance. In Proceedings of 3rd ACM Symposium on Parallel Algorithms and Architectures, pages 125-136, 1991.
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