Fukuda K.: cdd reference manual, version 0.56. ETH Zentrum, Zurich, Switzerland (1995) Home/Search Document Not in Database Summary Related Articles Check |
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Solitaire Cones - Avis, Deza (1996) (1 citation) (Correct)
....game on the toric closure of the 1 by 4 board Finding all facets of the cone SB is an example of a convex hull or vertex enumeration problem, for which various computer programs are available. The results in this paper were obtained using the double description method cdd implemented by Fukuda [13], and the reverse search method lrs implemented by Avis [3] We made use of these codes to completely generate all facets for some small boards as reported in later sections (such as the 930 048 facets for the toric closure of the 4 by 4 board) For realistically sized boards the corresponding ....
Fukuda K.: cdd reference manual, version 0.56. ETH Zentrum, Zurich, Switzerland (1995)
How Good are Convex Hull Algorithms? - Avis, Bremner (1995) (Correct)
....matrix to some canonical form, and there is the question of how to treat the right hand side vector. Here we assume that the input constraints are taken as is, and the right hand side entry is treated as the most significant digit of the coefficient vector (this is modelled on the program cdd [9]) random Insert the halfspaces in random order. maxcutoff (mincutoff) Insert the halfspace that causes the maximum (minimum) number of vertices and extreme rays to become infeasible. Previous experiments (see [9] have shown that there is no unique one of these orders that works well on all ....
....significant digit of the coefficient vector (this is modelled on the program cdd [9] random Insert the halfspaces in random order. maxcutoff (mincutoff) Insert the halfspace that causes the maximum (minimum) number of vertices and extreme rays to become infeasible. Previous experiments (see [9]) have shown that there is no unique one of these orders that works well on all problems. Theorem 5 The polytope K d , d 3, has size N = 4d 3 2d and any insertion algorithm to enumerate the vertices of K d creates intermediate polytopes of size Omega Gammaz 3 p N ) in the worst case when ....
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K. Fukuda. cdd Reference manual, version 0.52b. EPFL, Lausanne, Switzerland.
On Skeletons, Diameters and Volumes of Metric Polyhedra - Deza, Deza, Fukuda (1996) (Correct)
....is enough to compute all the vertices belonging to one facet. In [21] Grishukhin used this technique to compute the 41 orbits of extreme rays under permutations of the metric cone on 7 nodes. This vertex enumeration problem was solved using the double description method cdd implemented by Fukuda [20]. The algorithm first constructs a simplex starting with a non degenerate subset of d 1 inequalities where d is the dimension, then at each step one inequality is inserted. The efficiency of this algorithm highly depends on the order in which the inequalities are inserted. It is observed that ....
....cocliques of cocliques of facets and so on. This ordering gave us much better results that the classical lexico graphic, min cut off and max cut off ordering which respectively selects a facet which cuts off the minimum, respectively maximum, number of vertices of the intermediate polytope, see [20]. This ordering by maximal cocliques of the dual skeleton gave also excellent results for the computation of the Solitaire cone and its relatives, see [5] In all those cases, including the metric polytope, the maximal size of the intermediate polyhedra was less than twice the size of the final ....
Fukuda K.: cdd reference manual, version 0.56. ETH Zentrum, Zurich, Switzerland (1995)
The Quickhull Algorithm for Convex Hulls - Barber, Dobkin, Huhdanpaa (1995) (89 citations) (Correct)
....The Double Description Method is the dual of the Beneath Beyond Algorithm [36] It is the earliest incremental method for computing the convex hull. It is an excellent choice in high dimensions when the number of facets is much smaller than the maximum number of facets for r vertices (f r ) 3] [25]. 2. The Quickhull Algorithm We assume that the input points are in general position (i.e. no set of d 1 points define a (d Gamma 1) flat) so that their convex hull is a simplicial complex [39] We represent a d dimensional convex hull by its vertices and (d Gamma 1) dimensional faces (the ....
K. Fukuda. cdd Reference Manual. ftp://ifor13.ethz.ch/pub/fukuda/cdd, 1995.
How Good are Convex Hull Algorithms? - Avis, Bremner, Seidel (1997) (Correct)
....1: Availability of Software and Data by anonymous ftp and WWW. All of the software and data files described in this paper are available by anonymous ftp, and on the world wide web. See Table 1 for details. cddf and cddr are version 0. 73 of Fukuda s implementation of the double description method [19], compiled respectively to use floating point and exact rational arithmetic. porta is version 1.2.1 of Christof, Loebel, and Stoer s implementation of the double description method. qhull is Barber and Huhdanpaa s implementation of Quickhull (a variant of the beneath and beyond algorithm) ....
K. Fukuda. cdd Reference manual, version 0.55. EPFL, Lausanne, Switzerland.
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