On the Complexity of Optimization Problems for 3-Dimensional Convex Polyhedra and Decision Trees

On the Complexity of Optimization Problems for 3-Dimensional Convex Polyhedra and Decision Trees (1995)

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by Gautam Das , Michael T. Goodrich

Venue:	Comput. Geom. Theory Appl
Citations:	16 - 0 self

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Datum	Value	Source
TITLE	On the Complexity of Optimization Problems for 3-Dimensional Convex Polyhedra and Decision Trees	user correction - Legacy Corrections
AUTHOR NAME	Gautam Das	SVM HeaderParse 0.1
AUTHOR AFFIL	y	SVM HeaderParse 0.2
AUTHOR NAME	Michael T. Goodrich	SVM HeaderParse 0.1
AUTHOR AFFIL	z; Dept. of Math Sciences Dept. of Computer Science; Univ. of Memphis Johns Hopkins Univ.	SVM HeaderParse 0.2
AUTHOR ADDR	Memphis, TN 38152 Baltimore, MD 21218	SVM HeaderParse 0.1
ABSTRACT	We show that several well-known optimization problems involving 3-dimensional convex polyhedra and decision trees are NP-hard or NP-complete. One of the techniques we employ is a linear-time method for realizing a planar 3-connected triangulation as a convex polyhedron, which may be of independent interest. Key words: Convex polyhedra, approximation, Steinitz's theorem, planar graphs, art gallery theorems, decision trees. 1 Introduction Convex polyhedra are fundamental geometric structures (e.g., see [20]). They are the product of convex hull algorithms, and are key components for problems in robot motion planning and computer-aided geometric design. Moreover, due to a beautiful theorem of Steinitz [20, 38], they provide a strong link between computational geometry and graph theory, for Steinitz shows that a graph forms the edge structure of a convex polyhedra if and only if it is planar and 3-connected. Unfortunately, algorithmic problems dealing with 3-dimensional convex polyhedra ...	user correction - Legacy Corrections
YEAR	1995	user correction - Legacy Corrections
VENUE	Comput. Geom. Theory Appl	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	8--123	INFERENCE
VOLUME	8	INFERENCE
CITATIONS	38 found	ParsCit 1.0