Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
G.L. Miller , Sch. of Comput. Sci., Carnegie Mellon Univ., Pittsburgh, PA, USA
S.-H. Teng , Sch. of Comput. Sci., Carnegie Mellon Univ., Pittsburgh, PA, USA
A class of graphs called k-overlap graphs is proposed. Special cases of k-overlap graphs include planar graphs, k-nearest neighbor graphs, and earlier classes of graphs associated with finite element methods. A separator bound is proved for k-overlap graphs embedded in d dimensions. The result unifies several earlier separator results. All the arguments are based on geometric properties of embedding. The separator bounds come with randomized linear-time and randomized NC algorithms. Moreover, the bounds are the best possible up to the leading term.
randomized NC algorithms, geometric embedding, randomized linear time algorithms, graph separators, k-overlap graphs, planar graphs, k-nearest neighbor graphs, finite element methods, separator bound
G.L. Miller, S.-H. Teng, S.A. Vavasis, "A unified geometric approach to graph separators",  Proceedings 32nd Annual Symposium of Foundations of Computer Science, vol. 00, no. , pp. 538-547, 1991, doi:10.1109/SFCS.1991.185417