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Optimal enclosing regions in planar graphs

โœ Scribed by Daniel Bienstock; Clyde L. Monma


Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
942 KB
Volume
19
Category
Article
ISSN
0028-3045

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Given a set P of n points in the plane, we consider the problem of finding a planar rectilinear annulus of minimum width which encloses the set P. We present an optimal O(n log n) algorithm for this problem.

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This paper generalizes a theorem of Thomassen on paths in planar graphs. As a corollary, it is shown that every 4-connected planar graph has a Hamilton path between any two specified vertices x, y and containing any specified edge other than xy.