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877
A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra
, 1990
"... We present a new piv otbased algorithm which can be used with minor modification for the enumeration of the facets of the convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary dimension. The algorithm has the following prope ..."
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Cited by 223 (29 self)
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We present a new piv otbased algorithm which can be used with minor modification for the enumeration of the facets of the convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary dimension. The algorithm has the following
The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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to linear hybrid systems. In particular, we consider symbolic modelchecking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We
Submodular functions, matroids and certain polyhedra
, 2003
"... The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts is that all ..."
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Cited by 355 (0 self)
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of linear programming. It turns out to be useful to regard “pure matroid theory”, which is only incidentally related to the aspects of algebra which it abstracts, as the study of certain classes of convex polyhedra. (1) A matroid M = (E,F) can be defined as a finite set E and a nonempty family F of so
Cones of matrices and setfunctions and 01 optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1991
"... It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection a ..."
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Cited by 347 (7 self)
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It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection
Beyond Convexity: Scanning ‘NonConvex Polyhedra’
"... The enumeration of points contained in an algebraically specified domain is one of the key algorithmic problems in the transformation of scientific programs. However, basic scanning algorithms accept only single convex polyhedra, requiring specialized techniques and causing runtime overhead if the ..."
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The enumeration of points contained in an algebraically specified domain is one of the key algorithmic problems in the transformation of scientific programs. However, basic scanning algorithms accept only single convex polyhedra, requiring specialized techniques and causing runtime overhead
Reverse Search for Enumeration
 Discrete Applied Mathematics
, 1993
"... The reverse search technique has been recently introduced by the authors for efficient enumeration of vertices of polyhedra and arrangements. In this paper, we develop this idea in a general framework and show its broader applications to various problems in operations research, combinatorics, and ..."
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Cited by 205 (26 self)
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The reverse search technique has been recently introduced by the authors for efficient enumeration of vertices of polyhedra and arrangements. In this paper, we develop this idea in a general framework and show its broader applications to various problems in operations research, combinatorics
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
 Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science
, 2002
"... The domain of convex polyhedra is employed in several systems for the analysis and verification of hardware and software components. ..."
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Cited by 69 (9 self)
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The domain of convex polyhedra is employed in several systems for the analysis and verification of hardware and software components.
On Convex Representation of Convex Polyhedra
 Proc. of the First International Congress of Mathematical Software
"... Every convex polyhedron in the Euclidean space Rd admits both Hrepresentation and Vrepresentation. When working with convex polyhedra, in particular largescale ones in high dimensions, it is useful to have a canonical representation that is minimal and unique up to some elementary operations. Such ..."
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Cited by 12 (2 self)
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Every convex polyhedron in the Euclidean space Rd admits both Hrepresentation and Vrepresentation. When working with convex polyhedra, in particular largescale ones in high dimensions, it is useful to have a canonical representation that is minimal and unique up to some elementary operations
Results 1  10
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877