Sparse topologies with small spectrum size

Theoretical Computer Science

Volumn 307, Issue 3, 2003, Pages 549-565

  Elsasser R ^a   Kralovic R ^a,b   Monien, B ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

^b Physics and Informatics   (Slovakia)

Author keywords

Interconnection topologies; Laplacian of a graph; Spectra of graphs

Indexed keywords

DISTRIBUTED COMPUTER SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LAPLACE TRANSFORMS; THEOREM PROVING;

SPARSE GRAPHS;

GRAPH THEORY;

EID: 0141887059     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(03)00237-8     Document Type: Article

References (20)

1. S.B. Akers, D. Harel, B. Krishnamurthy, The Star Graph: An Attractive Alternative to the n -Cube, Proc. Internat. Conf. on Parallel Processing, 1987, pp. 393-400.
2. Akers S.B., Krishnamurthy B. A group-theoretic model for symmetric interconnection networks. IEEE Trans. Comput. 38:1989;555-565.
3. Biggs N.L. Algebraic Graph Theory. 2nd Edition:1993;Cambridge University Press, Cambridge.
4. Brouwe A.E., Cohen A.M., Neumaier A. Distance-Regular Graphs. 1989;Springer, Berlin.
5. Chung F.R.K. Spectral Graph Theory. 1994;American Mathematical Society, Providence, RI.
6. Cvetković D.M., Doob M., Sachs H. Spectra of Graphs, Theory and Application. 1980;Academic Press, New York.
7. Cybenko G. Load balancing for distributed memory multiprocessors. J. Parallel Distributed Comput. 7:1989;279-301.
8. T. Decker, B. Monien, R. Preis, Towards Optimal Load Balancing Topologies, Proc. 6th EuroPar Conf., Lecture Notes in Computer Science, Vol. 1900, Springer, Berlin, 2000, pp. 277-287.
9. Delorme C., Tillich J.P. The spectrum of DeBruijn and Kautz Graphs. European J. Combin. 19:1998;307-319.
10. Diekmann R., Frommer A., Monien B. Efficient schemes for nearest neighbor food balancing. Parallel Comput. 25:1999;789-812.
11. R. Elsässer, A. Frommer, B. Monien, R. Preis, Optimal and alternating direction load balancing, EuroPar'99, Lecture Notes in Computer Science, Vol. 1685, Springer, Berlin, 1999, pp. 280-290.
12. R. Elsässer, R. Královič, B. Monien, Scalable sparse topologies with small spectrum, STACS'01, Lecture Notes in Computer Science, Vol. 2010, Springer, Berlin, 2001, pp. 218-229.
13. Flatto L., Odlyzko A.M., Wales D.B. Random shuffles and group representations. Ann. Probab. 13:1985;154-178.
14. B. Ghosh, S. Muthukrishnan, M.H. Schultz, First and Second order diffusive methods for rapid, coarse, distributed load balancing, SPAA (1996) 72-81.
15. Hu Y.F., Blake R.J. An improved diffusion algorithm for dynamic load balancing. Parallel Comput. 25:1999;417-444.
16. Hu Y.F., Blake R.J., Emerson D.R. An optimal migration algorithm for dynamic load balancing. Concurrency Prac. Exp. 10:1998;467-483.
17. Hubaut X.L. Strongly regular graphs. Discrete Math. 13:1975;357-381.
18. G. Schmidt, Über die Spektren wichtiger Graphklassen, Bachelor Thesis, 2001.
19. J.-P. Tillich, The spectrum of the double-rooted tree, personal communication.
20. Xu C., Lau F.C.M. Load Balancing in Parallel Computers. 1997;Kluwer, Dordrecht.