Edge-Guarding Orthogonal Polyhedra

Authors

Nadia M. Benbernou, Massachusetts Institute of Technology
Erik D. Demaine, MIT Computer Science & Artificial Intelligence Laboratory
Martin L. Demaine, MIT Computer Science & Artificial Intelligence Laboratory
Anastasia Kurdia
Joseph O'Rourke, Smith CollegeFollow
Godfried Toussaint, Harvard University
Jorge Urrutia, Universidad Nacional Autónoma de México
Giovanni Viglietta, Università di Pisa

Document Type

Conference Proceeding

Publication Date

12-1-2011

Publication Title

Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011

Abstract

We address the question: How many edge guards are needed to guard an orthogonal polyhedron of e edges, r of which are reflex? It was previously established [3] that e/12 are sometimes necessary and e/6 always suf- fice. In contrast to the closed edge guards used for these bounds, we introduce a new model, open edge guards (excluding the endpoints of the edge), which we argue are in some sense more natural in this context. After quantifying the relationship between closed and open edge guards, we improve the upper bound to show that, asymptotically, (11/72)e (open or closed) edge guards suffice, or, in terms of r, that (7/12)r suffice. Along the way, we establish tight bounds relating e and r for orthogonal polyhedra of any genus.

Rights

© the authors

Comments

Archived as published.

Recommended Citation

Benbernou, Nadia M.; Demaine, Erik D.; Demaine, Martin L.; Kurdia, Anastasia; O'Rourke, Joseph; Toussaint, Godfried; Urrutia, Jorge; and Viglietta, Giovanni, "Edge-Guarding Orthogonal Polyhedra" (2011). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/183