@inproceedings{Kelly1996closure,
author = {Wayne Kelly and
William Pugh and
Evan Rosser and
Tatiana Shpeisman},
title = {Transitive Closure of Infinite Graphs and Its Applications},
pages = {126-140},
editor = {Chua-Huang Huang and
P. Sadayappan and
Utpal Banerjee and
David Gelernter and
Alexandru Nicolau and
David A. Padua},
booktitle = {Languages and Compilers for Parallel Computing, 8th International
Workshop, LCPC'95, Columbus, Ohio, USA, August 10-12, 1995,
Proceedings},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
volume = {1033},
year = {1996},
isbn = {3-540-60765-X},
}
@inproceedings{Beletska2009,
author = {Beletska, Anna and Barthou, Denis and Bielecki, Wlodzimierz and Cohen, Albert},
title = {Computing the Transitive Closure of a Union of Affine Integer Tuple Relations},
booktitle = {COCOA '09: Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications},
year = {2009},
isbn = {978-3-642-02025-4},
pages = {98--109},
location = {Huangshan, China},
doi = {10.1007/978-3-642-02026-1_9},
publisher = {Springer-Verlag},
address = {Berlin, Heidelberg},
}
@book{Schrijver1986,
author = "Schrijver, Alexander",
title = "Theory of Linear and Integer Programming",
publisher = "John Wiley \& Sons",
year = 1986
}
@article{Tarjan1972,
author = {Tarjan, Robert},
journal = {SIAM Journal on Computing},
number = {2},
pages = {146--160},
publisher = {SIAM},
title = {Depth-First Search and Linear Graph Algorithms},
volume = {1},
year = {1972}
}
@TechReport{ Omega_calc,
author = "Wayne Kelly and Vadim Maslov and William Pugh and Evan Rosser and Tatiana Shpeisman and Dave Wonnacott",
title = "The {Omega} Calculator and Library",
month = nov,
institution = "University of Maryland",
year = 1996
}
@TechReport{ Omega_lib,
author = "Wayne Kelly and Vadim Maslov and William Pugh and Evan Rosser and Tatiana Shpeisman and Dave Wonnacott",
title = "The {Omega} Library",
month = nov,
institution = "University of Maryland",
year = 1996
}
@unpublished{Verdoolaege2009isl,
author = "Verdoolaege, Sven",
title = "An integer set library for program analysis",
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",
month = Apr,
year = "2009",
url = "https://lirias.kuleuven.be/handle/123456789/228373",
}
@article{Barthou2000MSE,
author = {Barthou, Denis and Cohen, Albert and Collard, Jean-Fran\c{c}ois},
title = {Maximal Static Expansion},
journal = {Int. J. Parallel Program.},
volume = {28},
number = {3},
year = {2000},
issn = {0885-7458},
pages = {213--243},
doi = {10.1023/A:1007500431910},
publisher = {Kluwer Academic Publishers},
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,
}