Paper by Erik D. Demaine

Reference:

Nadia M. Benbernou, Erik D. Demaine, Martin L. Demaine, Michael Hoffmann, Mashhood Ishaque, Diane L. Souvaine, and Csaba D. Tóth, “Disjoint Segments have Convex Partitions with 2-Edge Connected Dual Graphs”, in Proceedings of the 19th Canadian Conference on Computational Geometry (CCCG 2007), Ottawa, Ontario, Canada, August 20–22, 2007, pages 13–16.

Abstract:

The empty space around n disjoint line segments in the plane can be partitioned into n + 1 convex faces by extending the segments in some order. The dual graph of such a partition is the plane graph whose vertices correspond to the n + 1 convex faces, and every segment endpoint corresponds to an edge between the two incident faces on opposite sides of the segment. We construct, for every set of n disjoint line segments in the plane, a convex partition whose dual graph is 2-edge connected.

Updates:

Unfortunately this paper is flawed. Read our erratum (which appears in CCCG 2008, page 223).

Length:

The paper is 4 pages.

Availability:

The paper is available in PostScript (459k), gzipped PostScript (186k), and PDF (146k).

See information on file formats.

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