Incomplete hypercubes: Embeddings of tree-related networks

Journal of Parallel and Distributed Computing

Volumn 26, Issue 1, 1995, Pages 36-47

  Ohring, Sabine ^a   Das, Sajal K ^a  

^a UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002621745     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1006/jpdc.1995.1045     Document Type: Article

References (43)

1. J. R. Armstrong and F. G. Gary, Fault diagnosis in boolean n-cube array. IEEE Trans. Comput. C-30(8), 590-596 (Aug. 1981).
2. S. B. Akers and B. Krishnamurthy, A group-theoretic model for symmetric interconnection networks. IEEE Trans. Comput. 38(4), 555-566 (Apr. 1989).
3. V. Auletta, A. A. Rescigno, and V. Scarano, On the fault tolerance and computational capabilities of the supercube. In Proceedings of the 4th Italian Conference on Theoretical Computer Science, 1992, pp. 38-52.
4. L. Bhuyan and D. P. Agrawal, Generalized hypercubes and hyperbus structures for a computer network. IEEE Trans. Comput. C-33, 323-333 (1984).
5. S. N. Bhatt, F. Chung, F. T. Leighton, and A. Rosenberg, Optimal simulation of tree machines. In Proc. 27th Annual Symposium on Foundations of Computer Science, 1986, pp. 274-282.
6. S. N. Bhatt, F. R. K. Chung, F. T. Leighton, and A. L. Rosenberg, Efficient embeddings of trees in hypercubes. SIAMJ. Comput. 21(1), 151-162 (1992).
7. A. J. Boals, A. K. Gupta, and N. A. Sherwani, Incomplete hypercubes: Embeddings and algorithms. Manuscript, Sept. 1992.
8. S. N. Bhatt and I. Ipsen, How to embed trees in hypercubes. Technical report, rr-443, Department of Computer Science, Yale University, New Haven, CT, 1985.
9. J. L. Bentley and H. T. Kung, A tree machine for searching problems. In Proceedings International Parallel Processing Conference, 1979, pp. 257-266.
10. J. C. Bermond and C. Peyrat, de Bruijn and Kautz networks: A competitor for the hypercube? In Hypercubes and Distributed Computers. Elsevier, Amsterdam, 1989, pp. 279-293.
11. G. Chartrand and L. Lesniak, Graphs and Digraphs, 2nd ed. Wadsworth & Brooks, Belmont, CA, 1986.
12. S. K. Das and A. K. Baneijee, Hyper Petersen network: Yet another hypercube-like topology. In Proceedings of the 4th Symposium on the Frontiers of Massively Parallel Computation (Frontiers' 92), McLean, Virginia, Oct. 1992. Computer Society Press, New York, 1992, pp. 270-277.
13. S. K. Das, J. Ghosh, and N. Deo, Stirling networks: A versatile combinatorial topology for multiprocessor systems. Discrete Appl. Math. (Special Double Volume on Interconnection Networks) 37/38, 119-146 (July 1992).
14. S. K. Das and A. Mao, Efficient communications in generalized incomplete hypercubes. Technical report, Center for Research in Parallel and Distributed Computing, Department of Computer Sciences, University of North Texas, June 1993.
15. S. K. Das and A. Mao, A theoretical interconnection network model and the Hamming cube networks. In Proceedings of the 8th International Parallel Processing Symposium, Cancún, Mexico, Apr. 1994, pp. 18-22.
16. S. K. Das, S. Ohring, and A. K. Baneijee, Embeddings into hyper Petersen networks: Yet another hypercube-like interconnection topology. J. VLSI Design (SpecialIssue on Interconnection Networks) 2(4), 335-352 (1994).
17. A. M. Despain and D. A. Patterson, X-tree: A tree structured multiprocessor computer architecture. In Proceedings 5th Annual Symposium on Computer Architecture, 1978, pp. 144-151.
18. K. Efe, Embedding mesh of trees in the hypercube. J. Parallel Distribut. Comput. 11, 222-230 (1991).
19. E. Ganesan and D. K. Pradhan, The hyper-de Bruijn multiprocessor networks. In Proceedings of the llth Conference on Distributed Computing Systems, Arlington, TX, May 1991, pp. 492-499. Also: The hyper-de Bruijn networks: Scalable versatile architecture. IEEE Trans. Parallel Distribut. Systems 4(9), 962-978 (1993).
20. C.-T. Ho and S. L. Johnsson, On the embedding of arbitrary meshes in boolean cubes with expansion two dilation two. In Proceedings of the 1987 International Conference on Parallel Processing, 1987.
21. C.-T. Ho, Optimal communication primitives and graph embeddings on hypercubes. Ph.D. thesis, Yale University, May 1990.
22. E. Horowitz and A. Zorat, The binary tree as an interconnection network: Applications to multiprocessor sytems and VLSI. IEEE Trans. Comput. 30, 247-253 (1981).
23. H. P. Katseff, Incomplete hypercubes. IEEE Trans. Comput. 37(5), 604-608 (May 1988).
24. F. T. Leighton, Parallel computing using mesh of trees. In Proceedings of the Workshop on Graph-Theoretic Concepts in Computer Science, 1983, pp. 200-218.
25. F. T. Leighton, Introduction to Parallel Algorithms and Architectures: Array s-Trees-Hypercubes. Morgan Kauf-mann, San Mateo, CA, 1992.
26. B. Monien and H. Sudborough, Embedding one interconnection network in another. In Computational Graph Theory. Springer-Verlag, Wien, 1990, pp. 257-282.
27. S. Ohring and S. K. Das, Embeddings of tree-related networks in incomplete hypercubes. In Proceedings of Parallel Architectures and Languages Europe (PARLE), Munich, Germany, June 1993, pp. 80-91. Also: Technical report, University of North Texas (CRPDC-92-20), University of Wuerzburg, Dec. 1992.
28. S. Ohring and S. K. Das, Dynamic embeddings of trees and quasi-grids into hyper-de Bruijn networks. In Proceedings of the 7th International Parallel Processing Symposium, Newport Beach, CA, Apr. 1993, pp. 519-523.
29. S. Ohring and S. K. Das, The folded Petersen network: A new communication-efficient multiprocessor topology. In Proceedings of the 1993 International Conference on Parallel Processing, Aug. 1993, Vol. I, PP- 311-314.
30. F. P. Preparata and J. Vuillemin, The cube-connected cycles: A versatile network for parallel computation. Comm. ACM 24(5), 300-309 (May 1981).
31. A. Sen, Supercube: An optimally fault tolerant network architecture. Acta Inform. 26, 741-748 (1989).
32. M. R. Samatham and D. K. Pradhan, The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI. IEEE Trans. Comput. 38(4), 567-581 (Apr. 1989).
33. Y. Saad and M. H. Schultz, Topological properties of hypercubes. In IEEE Trans. Comput. 37(7), 867-872 (1988).
34. H. S. Stone, Parallel processing with the perfect shuffle. IEEE Trans. Comput. C-20(2), 153-161 (Feb. 1971).
35. Q. F. Stout, Sorting, merging, selecting, and filtering on tree and pyramid machines. In Proceedings of the 1983 International Conference on Parallel Processing. IEEE Computer Society, Los Alamitos, CA, 1983, pp. 214-221.
36. Q. F. Stout, Hypercubes and pyramids. In V. Cantoni and S. Levialdi (Eds.). Pyramidal Systems for Computer Vision. Springer, Heidelberg, 1986, pp. 75-89.
37. N. -F. Tzeng, H.-L. Chen, and P.-J. Chuang, Embeddings in incomplete hypercubes. In Proceedings of the 1990 International Conference on Parallel Processing, 1990, Vol. III, pp. 335-339.
38. J.-Y. Tien and W.-P. Yang, Hierarchical spanning trees and distributing on incomplete hypercubes. Parallel Comput. 17, 1343-1360 (1991).
39. N.-F. Tzeng, Structural properties of incomplete hypercube computers. In Proceedings of the 10th International Conference on Distributed Computer Systems, Paris, France, May 28-June 1, 1990, pp. 262-269.
40. L. Uhr, Algorithm-Structured Computer Arrays and Networks: Architectures and Processes for Images, Perceps and Information. Academic Press, New York, 1984.
41. A. S. Wagner, Embedding all binary trees in the hypercube. In Proceedings of the Third IEEE Symposium Parallel and Distributed Processing, Dallas, TX, Dec. 1991, pp. 104-111.
42. A. Y. Wu, Embedding of tree networks into hypercubes. J. Parallel Distribut. Comput. 2, 238-249 (1985).
43. S.-M. Yuan, Topological properties of supercube. Inform. Process. Lett. 37, 241-245 (1991).