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
S. Teng, G. Miller and S. Vavasis, "A unified geometric approach to graph separators,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 538-547.