Algorithms pp 338-347 | Cite as

Planar separators and the Euclidean norm

  • Hillel Gazit
  • Gary L. Miller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 450)

Abstract

In this paper we show that every 2-connected embedded planar graph with faces of sizes d1.....df has a simple cycle separator of size 1.58 \(\sqrt {d_1^2 + \cdots + d_f^2 }\)and we give an almost linear time algorithm for finding these separators, O(no(n,n)). We show that the new upper bound expressed as a function of ‖G‖=\(\sqrt {d_1^2 + \cdots + d_f^2 }\)is no larger, up to a constant factor than previous bounds that where expressed in terms of \(\sqrt {d \cdot v}\)where d is the maximum face size and ν is the number of vertices and is much smaller for many graphs. The algorithms developed are simpler than earlier algorithms in that they work directly with the planar graph and its dual. They need not construct or work with the face-incidence graph as in [Mil86, GM87, GM].

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Hillel Gazit
    • 1
  • Gary L. Miller
    • 2
  1. 1.Department of Computer ScienceDuke UniversityUSA
  2. 2.School of Computer Science Carnegie Mellon University & Dept of Computer ScienceUniversity of Southern CaliforniaUSA

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