[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 538-547

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

ABSTRACT

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.

INDEX TERMS

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

CITATION

S. Teng, G. Miller and S. Vavasis, "A unified geometric approach to graph separators,"

*[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS)*, San Juan, Puerto Rico, 1991, pp. 538-547.

doi:10.1109/SFCS.1991.185417

CITATIONS