Alon, N., P. Seymour, and R. Thomas. A separator theorem for non-planar graphs. In *Proceedings of the 22th Annual ACM Symposium on Theory of Computing*, Maryland, May 1990. ACM.

Blelloch, G., A. Feldmann, O. Ghattas, J. Gilbert, G. Miller, D. R. O'Hallaron, E. Schwabe and J. Schewchuk, S.-H. Teng. (1996). Automated parallel solution of unstructured PDE problems. *CACM*, invited submission, to appear.

Clarkson, K., D. Eppstein, G. L. Miller, C. Sturtivant, and S.-H. Teng. Approximating center point with iterated radon points. In *Proceedings of 9th ACM Symposium on Computational Geometry*, pp. 91–98, San Diego, May, 1993.

Crawford, G. E. Elementary proof that the arithmetic mean of any number of positive quantities is greater than the geometric mean. *Proc. Edinburgh Math. Soc.*, 17:2–4, 1899–1900.

Djidjev, H. N. On the problem of partitioning planar graphs. *SIAM J. Alg. Disc. Math.*, 3(2):229–240, June 1982.

Donath, W. E. (1988). Logic partitioning. In B. T. Preas and M. J. Lorenzetti, eds., *Physical Design Automation of VLSI Systems*, pp. 65–86. Benjamin/Cummings.

Donath, W. E., and A. J. Hoffman. (1972). Algorithms for partitioning of graphs and computer logic based on eigenvectors of connection matrices. *IBM Technical Disclosure Bulletin*, 15:938–944.

Eppstein, D., G. L. Miller, and S.-H. Teng. (1993). A deterministic linear time algorithm for geometric separators and its applications. In *Proceedings of 9th ACM Symposium on Computational Geometry*, pp. 99–108, San Diego, May.

Farhat, C., and M. Lesoinne. (1993). Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics. Int. J. Num. Meth. Eng. 36:745–764.

Farhat, C., and H. Simon. (1993). TOP/DOMDEC—a software tool for mesh partitioning and parallel processing. Technical Report, NASA Ames Research Center.

Frieze, A. M., G. L. Miller, and S.-H. Teng. (1992). Separator based parallel divide and conquer in computational geometry. In *4th Annual ACM Symposium on Parallel Algorithms and Architectures*, pp 420–430.

Gazit, H. (1986). An improved algorithm for separating a planar graph. Manuscript, Department of Computer Science, University of Southern California.

Gazit, H., and G. L. Miller. A parallel algorithm for finding a separator in planar graphs. In *28st Annual Symposium on Foundation of Computation Science, IEEE*, 238–248, Los Angeles, October 1987.

George, J. A. (1973). Nested dissection of a regular finite element mesh. *SIAM J. Numerical Analysis*, 10:345–363.

George, A., and J. W. H. Liu. (1981). *Computer Solution of Large Sparse Positive Definite Systems*. Prentice-Hall.

Gilbert, J. R., J. P. Hutchinson, and R. E. Tarjan. (1984). A separation theorem for graphs of bounded genus. *J. Algorithms*, 5:391–407.

Gilbert, J. R., G. L. Miller, and S.-H. Teng. (1995). Geometric mesh partitioning: Implementation and experiments. In *International Conference of Parallel Processing*, pp 418–427.

Heath, M., and P. Raghavan. (1994). A cartesian parallel nested dissection algorithm. To appear in *SIAM Journal on Matrix Analysis and Applications*.

Hendrickson, B., and R. Leland. (1993). Multidimensional spectral load balancing. Technical Report, Sandia National Laboratories, SAND93-0074.

Hendrickson, B., and R. Leland. (1993). A multilevel algorithm for partitioning graphs. Technical Report SAND93-1301, Sandia National Laboratories, Albuquerque, NM.

Hendrickson, B., and R. Leland. (1993). The Chaco user's guide, Version 1.0. Technical Report SAND93-2339, Sandia National Laboratories, Albuquerque, NM.

Jordan, C. (1869). Sur les assemblages de lignes. *Journal Reine Angew. Math*, 70:185–190.

Kernighan B. W., and S. Lin. (1970). An efficient heuristic procedure for partitioning graphs. *Bell Sys. Tech. J.*, 49:291–307.

Leighton, F. T. (1983). *Complexity Issues in VLSI*. Foundations of Computing. MIT Press, Cambridge, MA.

Leighton, F. T., and S. Rao. (1988). An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms. In *29th Annual Symposium on Foundations of Computer Science*, pp 422–431.

Leiserson, C. E. (1983). *Area Efficient VLSI Computation*. Foundations of Computing. MIT Press, Cambridge, MA.

Lipton, R. J., D. J. Rose, and R. E. Tarjan. (1979). “Generalized nested dissection”. *SIAM J. on Numerical Analysis*, 16:346–358.

Lipton, R. J., and R. E. Tarjan. (1979). “A separator theorem for planar graphs”. *SIAM J. of Appl. Math.*, 36(April), 177–189.

Miller, G. L. (1986). Finding small simple cycle separators for 2-connected planar graphs. *Journal of Computer and System Sciences*, 32(3)(June), 265–279.

Miller, G. L., S.-H. Teng, W. Thurston, and S. A. Vavasis. (1996). “Automatic Mesh Partitioning.” In A. George, J. Gilbert, and J. Liu, editors, *Sparse Matrix Computations: Graph Theory Issues and Algorithms*, IMA Volumes in Mathematics and its Applications. Springer-Verlag.

Miller, G. L., S.-H. Teng, W. Thurston, and S. A. Vavasis. (1996). Finite element meshes and geometric separators. *SIAM J. Scientific Computing*, to appear.

Nour-Omid, B., A. Raefsky, and G. Lyzenga. (1987). Solving finite element equations on concurrent computers. in A. K. Noor, ed., *Parallel Computations and Their Impact on Mechanics*, The American Society of Mechanical Engineers, AMD-Vol. 86, 209–228.

Pan, V., and J. Reif. (1985). Efficient parallel solution of linear systems. In *Proceedings of the 17th Annual ACM Symposium on Theory of Computing*, pages 143–152, Providence, RI, May. ACM.

Pothen, A., H. D. Simon, and K.-P. Liou. (1990). Partitioning sparse matrices with eigenvectors of graphs. *SIAM J. Mat. Anal. Appl.*, 11(3):430–452.

Simon, H. D. (1991). Partitioning of unstructured problems for parallel processing. *Computing Systems in Engineering* 2(2/3):135–148.

Teng, S.-H.. (1991). *Points, Spheres, and Separators: a unified geometric approach to graph partitioning*. Ph.D. Thesis, Carnegie Mellon University, CMU-CS-91-184.

Ungar, P. (1951). A theorem on planar graphs. *Journal London Math Soc.* 26:256–262.

Williams, R. D. (1991). Performance of dynamic load balancing algorithms for unstructured mesh calculations *Concurrency: Practice and Experience*, 3(5):457–481.