A unified geometric approach to graph separators

  • Authors:
  • Gary L. Miller;Shang-Hua Teng;Stephen A. Vavasis

  • Affiliations:
  • -;-;-

  • Venue:
  • SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
  • Year:
  • 1991

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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.