1 @inproceedings{Kelly1996closure,
2 author = {Wayne Kelly and
6 title = {Transitive Closure of Infinite Graphs and Its Applications},
8 editor = {Chua-Huang Huang and
14 booktitle = {Languages and Compilers for Parallel Computing, 8th International
15 Workshop, LCPC'95, Columbus, Ohio, USA, August 10-12, 1995,
17 publisher = {Springer},
18 series = {Lecture Notes in Computer Science},
21 isbn = {3-540-60765-X},
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},
29 isbn = {978-3-642-02025-4},
31 location = {Huangshan, China},
32 doi = {10.1007/978-3-642-02026-1_9},
33 publisher = {Springer-Verlag},
34 address = {Berlin, Heidelberg},
38 author = "Schrijver, Alexander",
39 title = "Theory of Linear and Integer Programming",
40 publisher = "John Wiley \& Sons",
45 author = {Tarjan, Robert},
46 journal = {SIAM Journal on Computing},
50 title = {Depth-First Search and Linear Graph Algorithms},
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",
59 institution = "University of Maryland",
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",
67 institution = "University of Maryland",
71 @unpublished{Verdoolaege2009isl,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",
77 url = "https://lirias.kuleuven.be/handle/123456789/228373",
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.},
89 doi = {10.1023/A:1007500431910},
90 publisher = {Kluwer Academic Publishers},
91 address = {Norwell, MA, USA},
94 @article{ Feautrier88parametric,
95 author = "P. Feautrier",
96 title = "Parametric Integer Programming",
97 journal = "RAIRO Recherche Op\'erationnelle",
105 author = {Feautrier, P.},
106 title = {Dataflow analysis of array and scalar references},
107 journal = {International Journal of Parallel Programming},
118 @INPROCEEDINGS{BouletRe98,
119 AUTHOR = {Pierre Boulet and Xavier Redon},
120 TITLE = {Communication Pre-evaluation in {HPF}},
121 BOOKTITLE = {EUROPAR'98},
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.
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.},
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},
150 EDITOR = {Bodik, R.},
153 series = "Lecture Notes in Computer Science",
154 publisher = "Springer-Verlag",
156 doi = "10.1007/b107108",
159 @article{Detlefs2005simplify,
160 author = {David Detlefs and Greg Nelson and James B. Saxe},
161 title = {Simplify: a theorem prover for program checking},
168 doi = {10.1145/1066100.1066102},
170 address = {New York, NY, USA},
173 @phdthesis{Nelson1980phd,
174 author = {Charles Gregory Nelson},
175 title = {Techniques for program verification},
177 order_no = {AAI8011683},
178 school = {Stanford University},
179 address = {Stanford, CA, USA},
182 @article{Woods2003short,
184 Journal = "J. Amer. Math. Soc.",
188 title = {{Short rational generating functions for lattice point
190 author = {Alexander Barvinok and Kevin Woods},
194 author = {Sven Verdoolaege},
195 title = {{\texttt{barvinok}}, version 0.22},
196 howpublished = {Available from \url{http://freshmeat.net/projects/barvinok/}},
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",
206 series = "Lecture Notes in Computer Science",
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},
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",
227 url = "citeseer.nj.nec.com/article/feautrier92some.html",
230 @misc{Bygde2010licentiate,
231 author = {Stefan Bygde},
232 title = {Static {WCET} Analysis based on Abstract Interpretation and Counting of Elements},
235 howpublished = {Licentiate thesis},
236 publisher = {M{\"{a}}lardalen University Press},
237 url = {http://www.mrtc.mdh.se/index.php?choice=publications&id=2144},
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},
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},
253 booktitle = {Digest of the 6th Workshop on Optimization for DSP and Embedded Systems, ODES-6},
254 editor = "Jagadeesh Sankaran and Vander Aa, Tom",
258 @misc{Galea2009personal,
259 author = "Fran\c{c}ois Galea",
260 title = "personal communication",
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/}},
271 @TECHREPORT{Cook1991implementation,
272 AUTHOR={William Cook and Thomas Rutherford and Herbert E. Scarf and David F. Shallcross},
273 TITLE={An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming},
276 INSTITUTION={Cowles Foundation, Yale University},
277 TYPE={Cowles Foundation Discussion Papers},
278 NOTE={available at \url{http://ideas.repec.org/p/cwl/cwldpp/990.html}},
282 @article{Karr1976affine,
283 author={ Michael Karr},
284 title={ Affine Relationships Among Variables of a Program },
285 journal={Acta Informatica},
289 publisher={Springer-Verlag},
293 @PhdThesis{Verhaegh1995PhD,
294 title = "Multidimensional Periodic Scheduling",
295 author = "Wim F. J. Verhaegh",
296 school = "Technische Universiteit Eindhoven",
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},
308 @misc{DeSmet2010personal,
309 author = "De Smet, Sven",
310 title = "personal communication",