Spanners of hypercube-derived networks

SIAM Journal on Discrete Mathematics

Volumn 9, Issue 1, 1996, Pages 37-54

  Heydemann, Marie Claude ^a   Peters, Joseph G ^b   Sotteau, Dominique ^a  

^a UFR 919 Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur   (France)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Butterflies; Cube connected cycles; De Bruijn graphs; Networks; Shuffle exchange graphs; Spanning subgraphs

Indexed keywords

INTERCONNECTION NETWORKS;

DILATATION; HYPERCUBE; ROUTING; SPANNING SUBGRAPH;

GRAPH THEORY;

EID: 0030352215     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480194266628     Document Type: Article

References (24)

1. F. ANNEXSTEIN, M. BAUMSLAG, AND A. ROSENBERG, Group action graphs and parallel architectures, SIAM J. Comput., 19 (1990), pp. 544-569.
2. B. AWERBUCH, Complexity of network synchronization, J. Assoc. Comput. Mach., 32 (1985), pp. 804-823.
3. B. AWERBUCH, A. BARATZ, AND D. PELEG, Efficient broadcast and light-weight spanners, manuscript, 1992.
4. H. BANDELT AND A. DRESS, Reconstruction of the shape of a tree from observed dissimilarity data, Adv. in Appl. Math., 7 (1986), pp. 309-343.
5. L. CAI, Tree 2-spanners, Tech. report CMPT TR 91-4, School of Computing Science, Simon Fraser University, Burnaby, BC, Canada, 1991.
6. L. CAI AND M. KEIL, Spanners in graphs with bounded degree, Res. Report 93-1, Department of Computational Science, University of Saskatchewan, Saskatchewan, Canada, 1993.
7. L. CHEW, There is a planar graph almost as good as the complete graph, in Proc. 2nd ACM Symposium on Computational Geometry, Yorktown Heights, NY, 1986, pp. 169-177.
8. D. DOBKIN, S. FRIEDMAN, AND K. SUPOWIT, Delaunay graphs are almost as good as complete graphs, Discrete Comput. Geom., 5 (1990), pp. 399-407.
9. R. FELDMANN AND P. MYSLIWIETZ, The shuffle exchange network has a Hamiltonian path, in Proc. Mathematical Foundations of Computer Science 92, Lecture Notes in Computer Science 629, Springer-Verlag, Berlin, 1992, pp. 246-254.
10. R. FELDMANN AND W. UNGER, The cube-connected cycles network is a subgraph of the butterfly network, Parallel Process. Lett., 2 (1992), pp. 13-19.
11. M.-C. HEYDEMANN AND D. SOTTEAU, A note on recursive properties of de Bruijn, Kautz and FFT digraphs, Inform. Process. Lett., 53 (1995), pp. 255-259.
12. F. T. LEIGHTON, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, Morgan Kaufmann, San Mateo, 1992.
13. A. LIESTMAN AND T. SHERMER, Additive spanners for hypercubes, Parallel Process. Lett., 1 (1991), pp. 35-42.
14. _, Grid spanners, Networks, 23 (1993), pp. 123-133.
15. D. MELIKSETIAN AND C. Y. CHEN, Optimal routing algorithm and the diameter of the cube-connected cycles, IEEE Trans. Parallel Distrib. Systems, 4 (1993), pp. 1172-1178.
16. B. MONIEN AND H. SUDBOROUGH, Embedding one interconnection network in another, Comput. Suppl., 7 (1990), pp. 257-282.
17. D. PELEG AND A. SCHAFFER, Graph spanners, J. Graph Theory, 13 (1989), pp. 99-116.
18. D. PELEG AND J. ULLMAN, An optimal synchronizer for the hypercube, in Proc. 6th ACM Symposium on Principles of Distributed Computing, Vancouver, BC, 1987, pp. 77-85.
19. D. PELEG AND E. UPFAL, A tradeoff between space and efficiency for routing tables, in Proc. 20th ACM Symposium on Theory of Computing, Chicago, IL, 1988, pp. 43-52.
20. A. ROSENBERG, Cycles in networks, Tech. report UM-CS-1991-020, Department of Computer and Information Science, University of Massachusetts, Amherst, MA, 1991.
21. D. RICHARDS AND A. LIESTMAN, Degree-constrained pyramid spanners, J. Parallel Distrib. Comput., 25 (1995), pp. 1-6.
22. R. STRONG, On Hamiltonian cycles in Cayley graphs of wreath products, Discrete Math., 65 (1987), pp. 75-80.
23. P. VAIDYA, A sparse graph almost as good as the complete graph on points in k dimensions, Discrete Comput. Geom., 6 (1991), pp. 369-381.
24. M. YOELI, Binary ring sequences, Amer. Math. Monthly, 69 (1962), pp. 852-855.