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71 @unpublished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"
,