address = {Norwell, MA, USA},
}
+@article{ Feautrier88parametric,
+ author = "P. Feautrier",
+ title = "Parametric Integer Programming",
+ journal = "RAIRO Recherche Op\'erationnelle",
+ volume = "22",
+ number = "3",
+ pages = "243--268",
+ year = "1988",
+}
+
+@Article{ Fea91,
+ author = {Feautrier, P.},
+ title = {Dataflow analysis of array and scalar references},
+ journal = {International Journal of Parallel Programming},
+ year = {1991},
+ OPTkey = {},
+ volume = {20},
+ number = {1},
+ OPTmonth = {},
+ pages = {23--53},
+ OPTnote = {},
+ OPTannote = {},
+}
+
+@INPROCEEDINGS{BouletRe98,
+ AUTHOR = {Pierre Boulet and Xavier Redon},
+ TITLE = {Communication Pre-evaluation in {HPF}},
+ BOOKTITLE = {EUROPAR'98},
+ PAGES = {263--272},
+ YEAR = 1998,
+ VOLUME = 1470,
+ series = {Lecture Notes in Computer Science},
+ PUBLISHER = {Springer-Verlag, Berlin},
+ ABSTRACT = { Parallel computers are difficult to program efficiently. We believe
+ that a good way to help programmers write efficient programs is to
+ provide them with tools that show them how their programs behave on
+ a parallel computer. Data distribution is the major performance
+ factor of data-parallel programs and so automatic data layout for
+ HPF programs has been studied by many researchers recently. The
+ communication volume induced by a data distribution is a good
+ estimator of the efficiency of this data distribution.
+
+ We present here a symbolic method to compute the communication
+ volume generated by a given data distribution during the program
+ writing phase (before compilation). We stay machine-independent to
+ assure portability. Our goal is to help the programmer understand
+ the data movements its program generates and thus find a good data
+ distribution. Our method is based on parametric polyhedral
+ computations. It can be applied to a large class of regular codes.},
+}
+
+@INPROCEEDINGS {Verdoolaege2005experiences,
+ AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Catthoor, Francky",
+ TITLE = {{E}xperiences with enumeration of integer projections of parametric polytopes},
+ BOOKTITLE = {{P}roceedings of 14th {I}nternational {C}onference on {C}ompiler {C}onstruction, {E}dinburgh, {S}cotland},
+ YEAR = {2005},
+ EDITOR = {Bodik, R.},
+ VOLUME = 3443,
+ pages = "91-105",
+ series = "Lecture Notes in Computer Science",
+ publisher = "Springer-Verlag",
+ address = "Berlin",
+ doi = "10.1007/b107108",
+}
+
+@article{Detlefs2005simplify,
+ author = {David Detlefs and Greg Nelson and James B. Saxe},
+ title = {Simplify: a theorem prover for program checking},
+ journal = {J. ACM},
+ volume = {52},
+ number = {3},
+ year = {2005},
+ issn = {0004-5411},
+ pages = {365--473},
+ doi = {10.1145/1066100.1066102},
+ publisher = {ACM},
+ address = {New York, NY, USA},
+ }
+
+@phdthesis{Nelson1980phd,
+ author = {Charles Gregory Nelson},
+ title = {Techniques for program verification},
+ year = {1980},
+ order_no = {AAI8011683},
+ school = {Stanford University},
+ address = {Stanford, CA, USA},
+ }
+
+@article{Woods2003short,
+ year = 2003,
+ Journal = "J. Amer. Math. Soc.",
+ volume = 16,
+ pages = "957--979",
+ month = apr,
+ title = {{Short rational generating functions for lattice point
+ problems}},
+ author = {Alexander Barvinok and Kevin Woods},
+}
+
+@misc{barvinok-0.22,
+ author = {Sven Verdoolaege},
+ title = {{\texttt{barvinok}}, version 0.22},
+ howpublished = {Available from \url{http://freshmeat.net/projects/barvinok/}},
+ year = 2006
+}
+
+@inproceedings{DeLoera2004Three,
+ title = "Three Kinds of Integer Programming Algorithms based on Barvinok's Rational Functions",
+ author = "De Loera, J. A. and D. Haws and R. Hemmecke and P. Huggins and R. Yoshida",
+ booktitle = "Integer Programming and Combinatorial Optimization: 10th International IPCO Conference",
+ year = "2004",
+ month = jan,
+ series = "Lecture Notes in Computer Science",
+ Volume = 3064,
+ Pages = "244-255",
+}
+
+@TechReport{Feautrier02,
+ author = {P. Feautrier and J. Collard and C. Bastoul},
+ title = {Solving systems of affine (in)equalities},
+ institution = {PRiSM, Versailles University},
+ year = 2002
+}
+
+@article{ Feautrier92multi,
+ author = "Paul Feautrier",
+ title = "Some Efficient Solutions to the Affine Scheduling Problem. {P}art {II}. Multidimensional Time",
+ journal = "International Journal of Parallel Programming",
+ volume = "21",
+ number = "6",
+ pages = "389--420",
+ year = "1992",
+ month = dec,
+ url = "citeseer.nj.nec.com/article/feautrier92some.html",
+}
+
+@misc{Bygde2010licentiate,
+ author = {Stefan Bygde},
+ title = {Static {WCET} Analysis based on Abstract Interpretation and Counting of Elements},
+ month = {March},
+ year = {2010},
+ howpublished = {Licentiate thesis},
+ publisher = {M{\"{a}}lardalen University Press},
+ url = {http://www.mrtc.mdh.se/index.php?choice=publications&id=2144},
+}
+
+@phdthesis{Meister2004PhD,
+ title = {Stating and Manipulating Periodicity in the Polytope Model. Applications to Program Analysis and Optimization},
+ author= {Beno\^it Meister},
+ school = {Universit\'e Louis Pasteur},
+ month = Dec,
+ year = {2004},
+}
+
+@inproceedings{Meister2008,
+ author = {Beno\^it Meister and Sven Verdoolaege},
+ title = {Polynomial Approximations in the Polytope Model: Bringing the Power
+ of Quasi-Polynomials to the Masses},
+ year = {2008},
+ booktitle = {Digest of the 6th Workshop on Optimization for DSP and Embedded Systems, ODES-6},
+ editor = "Jagadeesh Sankaran and Vander Aa, Tom",
+ month = apr,
+}
+
+@misc{Galea2009personal,
+ author = "Fran\c{c}ois Galea",
+ title = "personal communication",
+ year = 2009,
+ month = nov,
+}
+
+@misc{PPL,
+ author = "R. Bagnara and P. M. Hill and E. Zaffanella",
+ title = "The {Parma Polyhedra Library}",
+ howpublished = {\url{http://www.cs.unipr.it/ppl/}},
+}
+
+@TECHREPORT{Cook1991implementation,
+AUTHOR={William Cook and Thomas Rutherford and Herbert E. Scarf and David F. Shallcross},
+TITLE={An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming},
+YEAR=1991,
+MONTH=Aug,
+INSTITUTION={Cowles Foundation, Yale University},
+TYPE={Cowles Foundation Discussion Papers},
+NOTE={available at \url{http://ideas.repec.org/p/cwl/cwldpp/990.html}},
+NUMBER={990},
+}
+
+ @article{Karr1976affine,
+author={ Michael Karr},
+title={ Affine Relationships Among Variables of a Program },
+journal={Acta Informatica},
+Volume={6},
+pages={133-151},
+year={1976},
+publisher={Springer-Verlag},
+ignore={ },
+}
+
+@PhdThesis{Verhaegh1995PhD,
+ title = "Multidimensional Periodic Scheduling",
+ author = "Wim F. J. Verhaegh",
+ school = "Technische Universiteit Eindhoven",
+ year = 1995,
+}
+
+@INPROCEEDINGS{Seghir2006minimizing,
+ AUTHOR = "Rachid Seghir and Vincent Loechner",
+ TITLE = {Memory Optimization by Counting Points in Integer Transformations of Parametric Polytopes},
+ 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},
+ month = oct,
+ YEAR = {2006}
+}
+
+@misc{DeSmet2010personal,
+ author = "De Smet, Sven",
+ title = "personal communication",
+ year = 2010,
+ month = apr,
+}