1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
|
\begin{thebibliography}{10}
\bibitem{a-dcg}
N.~Amenta.
\newblock Directory of computational geometry.
\newblock
\htmladdnormallink{http://www.geom.uiuc.edu/software/cglist/}{http://www.geo%
m.uiuc.edu/software/cglist/}.
\bibitem{a-lrshome-01}
D.~Avis.
\newblock {\em lrs Homepage}.
\newblock
\htmladdnormallink{http://cgm.cs.mcgill.ca/\~{}avis/C/lrs.html}{http://cgm.c%
s.mcgill.ca/\~{}avis/C/lrs.html}.
\bibitem{abs-hgach-97}
D.~Avis, D.~Bremner, and R.~Seidel.
\newblock How good are convex hull algorithms.
\newblock {\em Computational Geometry: Theory and Applications}, 7:265--302,
1997.
\bibitem{af-pachv-92}
D.~Avis and K.~Fukuda.
\newblock A pivoting algorithm for convex hulls and vertex enumeration of
arrangements and polyhedra.
\newblock {\em Discrete Comput. Geom.}, 8:295--313, 1992.
\bibitem{b-pplhome}
R.~Bagnara.
\newblock Parma polyhedra library homepage, 2004.
\newblock \htmladdnormallink{http://www.cs.unipr.it/ppl/}
{http://www.cs.unipr.it/ppl/}.
\bibitem{bdh-qach-03}
C.B. Barber, D.P. Dobkin, and H.~Huhdanpaa.
\newblock {\em qhull, Version 2003.1}, 2003.
\newblock program and report available from
\htmladdnormallink{http://www.qhull.org/} {http://www.qhull.org/}.
\bibitem{bfm-pdmvf-97}
D.~Bremner, K.~Fukuda, and A.~Marzetta.
\newblock Primal-dual methods for vertex and facet enumeration.
\newblock In {\em Proc. 13th Annu. ACM Sympos. Comput. Geom.}, pages 49--56,
1997.
\bibitem{cl-porta-97}
T.~Christof and A.~L{\"o}bel.
\newblock {PORTA}: Polyhedron representation transformation algorithm (ver.
1.3.1), 1997.
\newblock \htmladdnormallink{http://www.zib.de/Optimization/Software/Porta/}
{http://www.zib.de/Optimization/Software/Porta/}.
\bibitem{dhhhty-latte-05}
J.~de~Loera, D.~Haws, R.~Hemmecke, Peter Huggins, J.~Tauzer, and R.~Yoshida.
\newblock {\em Latt{E}}.
\newblock University of California, Davis, 2005.
\newblock available from
\htmladdnormallink{http://www.math.ucdavis.edu/~latte/}{http://www.math.ucda%
vis.edu/~latte/}.
\bibitem{e-acg-87}
H.~Edelsbrunner.
\newblock {\em Algorithms in {C}ombinatorial {G}eometry}.
\newblock Springer-Verlag, 1987.
\bibitem{e-cgp}
J.~Erickson.
\newblock Computational geometry pages, list of software libraries and codes.
\newblock
\htmladdnormallink{http://compgeom.cs.uiuc.edu/\~{}jeffe/compgeom/}{http://c%
ompgeom.cs.uiuc.edu/\~{}jeffe/compgeom/}.
\bibitem{fg-lpfaq}
R.~Fourer and J.W. Gregory.
\newblock Linear programming frequently asked questions ({LP-FAQ}).
\newblock
\htmladdnormallink{http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programm%
ing-faq.html}
{http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html}.
\bibitem{f-pcfaq-98}
K.~Fukuda.
\newblock Polyhedral computation {FAQ}, 1998.
\newblock Both html and ps versions available from
\htmladdnormallink{http://www.ifor.math.ethz.ch/\~{}fukuda/fukuda.html}
{http://www.ifor.math.ethz.ch/\~{}fukuda/fukuda.html}.
\bibitem{f-fzctmacp-04}
K.~Fukuda.
\newblock From the zonotope construction to the {M}inkowski addition of convex
polytopes.
\newblock {\em Journal of Symbolic Computation}, 38(4):1261--1272, 2004.
\newblock pdf file available from
\htmladdnormallink{http://www.cs.mcgill.ca/\~{}fukuda/download/paper/minksum%
031007jsc.pdf}{http://www.cs.mcgill.ca/\~{}fukuda/download/paper/minksum031007%
jsc.pdf}.
\bibitem{fjt-cgf-05}
K.~Fukuda, A.~Jensen, and R.~Thomas.
\newblock Computing {G}r{\"o}bner fans.
\newblock Technical report.
\newblock In preparation.
\bibitem{fp-ddmr-96}
K.~Fukuda and A.~Prodon.
\newblock Double description method revisited.
\newblock In M.~Deza, R.~Euler, and I.~Manoussakis, editors, {\em Combinatorics
and Computer Science}, volume 1120 of {\em Lecture Notes in Computer
Science}, pages 91--111. Springer-Verlag, 1996.
\newblock ps file available from
\htmladdnormallink{ftp://ftp.ifor.math.ethz.ch/pub/fukuda/reports/ddrev96031%
5.ps.gz}{ftp://ftp.ifor.math.ethz.ch/pub/fukuda/reports/ddrev960315.ps.gz}.
\bibitem{j-gvum-05}
A.N. Jensen.
\newblock {\em Gfan version 0.1: A User's Manual}.
\newblock Department of Mathematical Sciences, University of Aarhus and
Institute for Operations Research, ETH Zurich, 2005.
\newblock available from
\htmladdnormallink{http://home.imf.au.dk/ajensen/software/gfan/gfan.html}{ht%
tp://home.imf.au.dk/ajensen/software/gfan/gfan.html}.
\bibitem{m-pdcip-97}
A.~Marzetta.
\newblock {\em pd -- {C}-implementation of the primal-dual algoirithm}, 1997.
\newblock code available from
\htmladdnormallink{http://www.cs.unb.ca/profs/bremner/pd/}
{http://www.cs.unb.ca/profs/bremner/pd/}.
\bibitem{mrtt-ddm-53}
T.S. Motzkin, H.~Raiffa, GL. Thompson, and R.M. Thrall.
\newblock The double description method.
\newblock In H.W. Kuhn and A.W.Tucker, editors, {\em Contributions to theory of
games, Vol. 2}. Princeton University Press, Princeton, RI, 1953.
\bibitem{m-cg-94}
K.~Mulmuley.
\newblock {\em Computational {G}eometry, {A}n {I}ntroduction {T}hrough
{R}andamized {A}lgorithms}.
\newblock Prentice-Hall, 1994.
\bibitem{r-topcom-05}
J.~Rambau.
\newblock {\em TOPCOM, a package for computing Triangulations Of Point
Configurations and Oriented Matroids}.
\newblock University of Bayreuth, 2005.
\newblock available from
\htmladdnormallink{http://www.uni-bayreuth.de/departments/wirtschaftsmathema%
tik/rambau/TOPCOM/}{http://www.uni-bayreuth.de/departments/wirtschaftsmathemat%
ik/rambau/TOPCOMl}.
\bibitem{w-msv-05}
C.~Weibel.
\newblock {\em Minksum version 1.1}.
\newblock Mathematics Institute, EPF Lausanne, 2005.
\newblock available from
\htmladdnormallink{http://roso.epfl.ch/cw/poly/public.php}{http://roso.epfl.%
ch/cw/poly/public.php}.
\bibitem{w-ldpo-93b}
D.K. Wilde.
\newblock A library for doing polyhedral operations.
\newblock Master's thesis, Oregon State University, Corvallis, Oregon, Dec
1993.
\newblock Also published in IRISA technical report PI 785, Rennes, France; Dec,
1993.
\end{thebibliography}
|
