Volume 450 of the series Lecture Notes in Computer Science pp 338347
Planar separators and the Euclidean norm
 Hillel GazitAffiliated withDepartment of Computer Science, Duke University
 , Gary L. MillerAffiliated withSchool of Computer Science Carnegie Mellon University & Dept of Computer Science, University of Southern California
Abstract
In this paper we show that every 2connected embedded planar graph with faces of sizes d _{1}.....d _{ f } 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 faceincidence graph as in [Mil86, GM87, GM].
 Title
 Planar separators and the Euclidean norm
 Book Title
 Algorithms
 Book Subtitle
 International Symposium SIGAL '90 Tokyo, Japan, August 16–18, 1990 Proceedings
 Pages
 pp 338347
 Copyright
 1990
 DOI
 10.1007/3540529217_83
 Print ISBN
 9783540529217
 Online ISBN
 9783540471776
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 450
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Hillel Gazit ^{(1)}
 Gary L. Miller ^{(2)}
 Author Affiliations

 1. Department of Computer Science, Duke University, USA
 2. School of Computer Science Carnegie Mellon University & Dept of Computer Science, University of Southern California, USA
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