Drawing huge graphs by algebraic multigrid optimization

Multiscale Modeling and Simulation

Volumn 1, Issue 4, 2003, Pages 645-673

  Koren, Yehuda ^a   Carmel, Liran ^a   Harel, David ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Algebraic multigrid; Fiedler vector; Force directed layout; Generalized eigenvalue problem; Graph drawing; Multiscale multilevel optimization; The Hall energy

Indexed keywords

ALGEBRA; DIRECTED GRAPHS; DRAWING (GRAPHICS); OPTIMIZATION;

ALGEBRAIC MULTIGRIDS; FIEDLER VECTORS; FORCE-DIRECTED LAYOUT; GENERALIZED EIGENVALUE PROBLEMS; GRAPH DRAWING; THE HALL ENERGY;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 85014929888     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/S154034590241370X     Document Type: Article

References (27)

1. S. T. Barnard and H. D. Simon, A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems, Concurrency: Practice & Experience, 6 (1994), pp. 101-117.
2. U. Brandes and T. Willhalm, Visualization of Bibliographic Networks with a Reshaped Landscape Metaphor, in Proceedings of the 4th Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym '02), Barcelona, Spain, 2002, ACM, New York, 2002, pp. 159-164.
3. A. Brandt, Algebraic multigrid theory: The symmetric case, Appl. Math. Comput., 19 (1986), pp. 23-56.
4. A. Brandt, S. McCormick, and J. Ruge, Algebraic Multigrid (AMG) for Automatic Multigrid Solution with Applications to Geodetic Computations, Technical report, Institute for Computational Studies, Fort Collins, CO, 1982.
5. R. Davidson and D. Harel, Drawing graphs nicely using simulated annealing, ACM Trans. on Graphics, 15 (1996), pp. 301-331.
6. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Prentice-Hall, Upper Saddle River, NJ, 1999.
7. P. Eades, A Heuristic for Graph Drawing, Congr. Numer., 42 (1984), pp. 149-160.
8. T. M. G. Fruchterman and E. Reingold, Graph drawing by force-directed placement, Software-Practice and Experience, 21 (1991), pp. 1129-1164.
9. P. Gajer, M. T. Goodrich, and S. G. Kobourov, A multi-dimensional approach to forcedirected layouts of large graphs, in Proceedings of the 8th International Symposium on Graph Drawing, Williamsburg, VA, 2000, Lecture Notes in Comput. Sci. 1984, Springer- Verlag, Berlin, 2000, pp. 211-221.
10. R. Hadany and D. Harel, A multi-scale method for drawing graphs nicely, Discrete Appl. Math., 113 (2001), pp. 3-21.
11. K. M. Hall, An r-dimensional quadratic placement algorithm, Management Sci., 17 (1970), pp. 219-229.
12. D. Harel and Y. Koren, A fast multi-scale method for drawing large graphs, J. Graph Algorithms Appl., 6 (2002), pp. 179-202.
13. D. Harel and Y. Koren, Graph drawing by high-dimensional embedding, in Proceedings of the 10th International Symposium on Graph Drawing, Irvine, CA, 2002, Lecture Notes in Comput. Sci. 2528, Springer-Verlag, Berlin, 2002, pp. 207-219.
14. I. Herman, G. Melancon, and M. S. Marshall, Graph visualisation and navigation in information visualisation, IEEE Trans. on Visualization and Computer Graphics, 6 (2000), pp. 24-43.
15. M. Juvan and B. Mohar, Optimal linear labelings and eigenvalues of graphs, Discrete Appl. Math., 36 (1992), pp. 153-168.
16. T. Kamada and S. Kawai, An algorithm for drawing general undirected graphs, Inform. Process. Lett., 31 (1989), pp. 7-15.
17. G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM J. Sci. Comput., 20 (1998), pp. 359-392.
18. M. Kaufmann and D. Wagner, eds., Drawing Graphs: Methods and Models, Lecture Notes in Comput. Sci. 2025, Springer-Verlag, Berlin, 2001.
19. Y. Koren, On spectral graph drawing, in Proceedings of the International Computing and Combinatorics Conference, Big Sky Resort, MT, Lecture Notes in Comput. Sci. 2697, Springer-Verlag, Berlin, 2003, pp. 496-508.
20. Y. Koren, L. Carmel, and D. Harel, ACE: A Fast Multiscale Eigenvectors Computation for Drawing Huge Graphs, Technical report MCS01-17, The Weizmann Institute of Science, Rehovot, Israel, 2001, http://citeseer.nj.nec.com/koren01ace.html
21. B. Mohar, The Laplacian spectrum of graphs, in Graph Theory, Combinatorics, and Applications, Vol. 2, Wiley, New York, 1991, pp. 871-898.
22. A. Quigley and P. Eades, FADE: Graph drawing, clustering, and visual abstraction, in Proceedings of the 8th International Symposium on Graph Drawing, Williamsburg, VA, 2000, Lecture Notes in Computer Sci. 1984, Springer-Verlag, Berlin, 2000, pp. 183-196.
23. J. W. Ruge and K. Stüben, Algebraic multigrid, in Multigrid Methods, Frontiers Appl. Math. 3, S. F. McCormick, ed., SIAM, Philadelphia, 1987, pp. 73-130.
24. J. Shi and J. Malik, Normalized cuts and image segmentation, IEEE Trans. on Pattern Analysis and Machine Intelligence, 22 (2000), pp. 888-905.
25. K. Stüben, An introduction to algebraic multigrid, in Multigrid, Appendix A, U. Trottenberg, C. W. Oosterlee, and A. Schuller, eds., Academic Press, London, 2000.
26. C. Walshaw, A multilevel algorithm for force-directed graph drawing, in Proceedings of the 8th International Symposium on Graph Drawing, Williamsburg, VA, 2000, Lecture Notes in Computer Sci. 1984, Springer-Verlag, Berlin, 2000, pp. 171-182.
27. D. S. Watkins, Fundamentals of Matrix Computations, John Wiley, New York, 1991.