1@inproceedings{Kelly1996closure,
2  author    = {Wayne Kelly and
3               William Pugh and
4               Evan Rosser and
5               Tatiana Shpeisman},
6  title     = {Transitive Closure of Infinite Graphs and Its Applications},
7  pages     = {126-140},
8  editor    = {Chua-Huang Huang and
9               P. Sadayappan and
10               Utpal Banerjee and
11               David Gelernter and
12               Alexandru Nicolau and
13               David A. Padua},
14  booktitle = {Languages and Compilers for Parallel Computing, 8th International
15               Workshop, LCPC'95, Columbus, Ohio, USA, August 10-12, 1995,
16               Proceedings},
17  publisher = {Springer},
18  series    = {Lecture Notes in Computer Science},
19  volume    = {1033},
20  year      = {1996},
21  isbn      = {3-540-60765-X},
22}
23
24@inproceedings{Beletska2009,
25  author = {Beletska, Anna and Barthou, Denis and Bielecki, Wlodzimierz and Cohen, Albert},
26  title = {Computing the Transitive Closure of a Union of Affine Integer Tuple Relations},
27  booktitle = {COCOA '09: Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications},
28  year = {2009},
29  isbn = {978-3-642-02025-4},
30  pages = {98--109},
31  location = {Huangshan, China},
32  doi = {10.1007/978-3-642-02026-1_9},
33  publisher = {Springer-Verlag},
34  address = {Berlin, Heidelberg},
35}
36
37@book{Schrijver1986,
38    author  =	"Schrijver, Alexander",
39    title   =	"Theory of Linear and Integer Programming",
40    publisher	=   "John Wiley \& Sons",
41    year    =	1986
42}
43
44@article{Tarjan1972,
45    author = {Tarjan, Robert},
46    journal = {SIAM Journal on Computing},
47    number = {2},
48    pages = {146--160},
49    publisher = {SIAM},
50    title = {Depth-First Search and Linear Graph Algorithms},
51    volume = {1},
52    year = {1972}
53}
54
55@TechReport{ Omega_calc,
56    author = "Wayne Kelly and Vadim Maslov and William Pugh and Evan Rosser and Tatiana Shpeisman and Dave Wonnacott",
57    title = "The {Omega} Calculator and Library",
58    month = nov,
59    institution = "University of Maryland",
60    year = 1996
61}
62
63@TechReport{ Omega_lib,
64    author = "Wayne Kelly and Vadim Maslov and William Pugh and Evan Rosser and Tatiana Shpeisman and Dave Wonnacott",
65    title = "The {Omega} Library",
66    month = nov,
67    institution = "University of Maryland",
68    year = 1996
69}
70
71@unpublished{Verdoolaege2009isl,
72  author = "Verdoolaege, Sven",
73  title = "An integer set library for program analysis",
74  note = "Advances in the Theory of Integer Linear Optimization and its Extensions,AMS 2009 Spring Western Section Meeting, San Francisco, California, 25-26 April 2009",
75  month = Apr,
76  year = "2009",
77  url = "https://lirias.kuleuven.be/handle/123456789/228373",
78}
79
80@article{Barthou2000MSE,
81  author = {Barthou, Denis and Cohen, Albert and Collard, Jean-Fran\c{c}ois},
82  title = {Maximal Static Expansion},
83  journal = {Int. J. Parallel Program.},
84  volume = {28},
85  number = {3},
86  year = {2000},
87  issn = {0885-7458},
88  pages = {213--243},
89  doi = {10.1023/A:1007500431910},
90  publisher = {Kluwer Academic Publishers},
91  address = {Norwell, MA, USA},
92}
93
94@article{ Feautrier88parametric,
95    author = "P. Feautrier",
96    title = "Parametric Integer Programming",
97    journal = "RAIRO Recherche Op\'erationnelle",
98    volume = "22",
99    number = "3",
100    pages = "243--268",
101    year = "1988",
102}
103
104@Article{ Fea91,
105  author =       {Feautrier, P.},
106  title =        {Dataflow analysis of array and scalar references},
107  journal =      {International Journal of Parallel Programming},
108  year =         {1991},
109  OPTkey =         {},
110  volume =       {20},
111  number =       {1},
112  OPTmonth =     {},
113  pages =        {23--53},
114  OPTnote =      {},
115  OPTannote =    {},
116}
117
118@INPROCEEDINGS{BouletRe98,
119  AUTHOR = {Pierre Boulet and Xavier Redon},
120  TITLE = {Communication Pre-evaluation in {HPF}},
121  BOOKTITLE = {EUROPAR'98},
122  PAGES = {263--272},
123  YEAR = 1998,
124  VOLUME = 1470,
125  series =	 {Lecture Notes in Computer Science},
126  PUBLISHER = {Springer-Verlag, Berlin},
127  ABSTRACT = {  Parallel computers are difficult to program efficiently.  We believe
128  that a good way to help programmers write efficient programs is to
129  provide them with tools that show them how their programs behave on
130  a parallel computer.  Data distribution is the major performance
131  factor of data-parallel programs and so automatic data layout for
132  HPF programs has been studied by many researchers recently.  The
133  communication volume induced by a data distribution is a good
134  estimator of the efficiency of this data distribution.
135
136  We present here a symbolic method to compute the communication
137  volume generated by a given data distribution during the program
138  writing phase (before compilation). We stay machine-independent to
139  assure portability.  Our goal is to help the programmer understand
140  the data movements its program generates and thus find a good data
141  distribution. Our method is based on parametric polyhedral
142  computations. It can be applied to a large class of regular codes.},
143}
144
145@INPROCEEDINGS {Verdoolaege2005experiences,
146  AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Catthoor, Francky",
147  TITLE = {{E}xperiences with enumeration of integer projections of parametric polytopes},
148  BOOKTITLE = {{P}roceedings of 14th {I}nternational {C}onference on {C}ompiler {C}onstruction, {E}dinburgh, {S}cotland},
149  YEAR = {2005},
150  EDITOR = {Bodik, R.},
151  VOLUME = 3443,
152    pages = "91-105",
153    series = "Lecture Notes in Computer Science",
154    publisher = "Springer-Verlag",
155    address = "Berlin",
156    doi = "10.1007/b107108",
157}
158
159@article{Detlefs2005simplify,
160 author = {David Detlefs and Greg Nelson and James B. Saxe},
161 title = {Simplify: a theorem prover for program checking},
162 journal = {J. ACM},
163 volume = {52},
164 number = {3},
165 year = {2005},
166 issn = {0004-5411},
167 pages = {365--473},
168 doi = {10.1145/1066100.1066102},
169 publisher = {ACM},
170 address = {New York, NY, USA},
171 }
172
173@phdthesis{Nelson1980phd,
174 author = {Charles Gregory Nelson},
175 title = {Techniques for program verification},
176 year = {1980},
177 order_no = {AAI8011683},
178 school = {Stanford University},
179 address = {Stanford, CA, USA},
180 }
181
182@article{Woods2003short,
183    year = 2003,
184    Journal = "J. Amer. Math. Soc.",
185    volume =  16,
186    pages = "957--979",
187    month = apr,
188    title = {{Short rational generating functions for lattice point
189        problems}},
190    author = {Alexander Barvinok and Kevin Woods},
191}
192
193@misc{barvinok-0.22,
194  author = {Sven Verdoolaege},
195  title = {{\texttt{barvinok}}, version 0.22},
196  howpublished = {Available from \url{http://freshmeat.net/projects/barvinok/}},
197  year = 2006
198}
199
200@inproceedings{DeLoera2004Three,
201    title = "Three Kinds of Integer Programming Algorithms based on Barvinok's Rational Functions",
202    author = "De Loera, J. A. and D. Haws and R. Hemmecke and P. Huggins and R. Yoshida",
203    booktitle = "Integer Programming and Combinatorial Optimization: 10th International IPCO Conference",
204    year = "2004",
205    month = jan,
206    series = "Lecture Notes in Computer Science",
207    Volume = 3064,
208    Pages = "244-255",
209}
210
211@TechReport{Feautrier02,
212  author = 	 {P. Feautrier and J. Collard and C. Bastoul},
213  title = 	 {Solving systems of affine (in)equalities},
214  institution =  {PRiSM, Versailles University},
215  year = 	 2002
216}
217
218@article{ Feautrier92multi,
219    author = "Paul Feautrier",
220    title = "Some Efficient Solutions to the Affine Scheduling Problem. {P}art {II}. Multidimensional Time",
221    journal = "International Journal of Parallel Programming",
222    volume = "21",
223    number = "6",
224    pages = "389--420",
225    year = "1992",
226    month = dec,
227    url = "citeseer.nj.nec.com/article/feautrier92some.html",
228}
229
230@misc{Bygde2010licentiate,
231   author = {Stefan Bygde},
232   title = {Static {WCET} Analysis based on Abstract Interpretation and Counting of Elements},
233   month = {March},
234   year = {2010},
235   howpublished = {Licentiate thesis},
236   publisher = {M{\"{a}}lardalen University Press},
237   url = {http://www.mrtc.mdh.se/index.php?choice=publications&id=2144},
238}
239
240@phdthesis{Meister2004PhD,
241	title = {Stating and Manipulating Periodicity in the Polytope Model. Applications to Program Analysis and Optimization},
242	author= {Beno\^it Meister},
243 	school = {Universit\'e Louis Pasteur},
244	month = Dec,
245	year  = {2004},
246}
247
248@inproceedings{Meister2008,
249  author = {Beno\^it Meister and Sven Verdoolaege},
250  title = {Polynomial Approximations in the Polytope Model: Bringing the Power
251  of Quasi-Polynomials to the Masses},
252  year = {2008},
253  booktitle = {Digest of the 6th Workshop on Optimization for DSP and Embedded Systems, ODES-6},
254  editor = "Jagadeesh Sankaran and Vander Aa, Tom",
255  month = apr,
256}
257
258@misc{Galea2009personal,
259    author = "Fran\c{c}ois Galea",
260    title = "personal communication",
261    year = 2009,
262    month = nov,
263}
264
265@misc{PPL,
266  author = "R. Bagnara and P. M. Hill and E. Zaffanella",
267  title = "The {Parma Polyhedra Library}",
268  howpublished = {\url{http://www.cs.unipr.it/ppl/}},
269}
270
271@TECHREPORT{Cook1991implementation,
272AUTHOR={William Cook and Thomas Rutherford and Herbert E. Scarf and David F. Shallcross},
273TITLE={An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming},
274YEAR=1991,
275MONTH=Aug,
276INSTITUTION={Cowles Foundation, Yale University},
277TYPE={Cowles Foundation Discussion Papers},
278NOTE={available at \url{http://ideas.repec.org/p/cwl/cwldpp/990.html}},
279NUMBER={990},
280}
281
282 @article{Karr1976affine,
283author={ Michael Karr},
284title={ Affine Relationships Among Variables of a Program },
285journal={Acta Informatica},
286Volume={6},
287pages={133-151},
288year={1976},
289publisher={Springer-Verlag},
290ignore={ },
291}
292
293@PhdThesis{Verhaegh1995PhD,
294	title = "Multidimensional Periodic Scheduling",
295	author = "Wim F. J. Verhaegh",
296	school = "Technische Universiteit Eindhoven",
297	year = 1995,
298}
299
300@INPROCEEDINGS{Seghir2006minimizing,
301  AUTHOR = "Rachid Seghir and Vincent Loechner",
302  TITLE = {Memory Optimization by Counting Points in Integer Transformations of Parametric Polytopes},
303  BOOKTITLE = {{P}roceedings of the {I}nternational {C}onference on {C}ompilers, {A}rchitectures, and {S}ynthesis for {E}mbedded Systems, CASES 2006, {S}eoul, {K}orea},
304  month = oct,
305  YEAR = {2006}
306}
307
308@misc{DeSmet2010personal,
309    author = "De Smet, Sven",
310    title = "personal communication",
311    year = 2010,
312    month = apr,
313}
314