Analysis of Backtrack Algorithms for Listing All Vertices and All Faces of a Convex Polyhedron
نویسندگان
چکیده
In this paper, we investigate the applicability of backtrack technique to solve the vertex enumeration problem and the face enumeration problem for a convex polyhedron given by a system of linear inequalities. We show that there is a linear-time backtrack algorithm for the face enumeration problem whose space complexity is polynomial in the input size, but the vertex enumeration problem requires a backtrack algorithm to solve a decision problem, called the restricted vertex problem, for each output, which is shown to be NP-complete. Some related NP-complete problems associated with a system of linear inequalities are also discussed, including the optimal vertex problems for polyhedra and arrangements of hyperplanes.
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ورودعنوان ژورنال:
- Comput. Geom.
دوره 8 شماره
صفحات -
تاریخ انتشار 1997