doc/barvinok.bib

   1 @string(ICPS = "ICPS, Universit\'e Louis Pasteur de Strasbourg, France")
   2
   3 @techreport{ Wilde1993,
   4     author = "D. K. Wilde",
   5     title = "A Library for doing polyhedral operations",
   6     number = "785",
   7     institution = "IRISA, Rennes, France",
   8     pages = "45 p.",
   9     year = 1993,
  10     url = "citeseer.nj.nec.com/article/wilde93library.html",
  11     note = "\\http://www.irisa.fr/EXTERNE/bibli/pi/pi785.html"
  12 }
  13
  14 @article{ Loechner97parameterized,
  15     author = "Vincent Loechner and Doran K. Wilde",
  16     title = "Parameterized Polyhedra and Their Vertices",
  17     journal = "International Journal of Parallel Programming",
  18     volume = "25",
  19     number = "6",
  20     pages = "525--549",
  21     year = "1997",
  22     month = dec,
  23     publisher = {Kluwer Academic Publishers},
  24     url = "citeseer.nj.nec.com/article/loechner95parameterized.html" }
  25
  26 @TechReport{ Loechner1999,
  27     author = "Vincent Loechner",
  28     month = mar,
  29     year = 1999,
  30     title = "PolyLib: A Library for Manipulating Parameterized Polyhedra",
  31     institution = ICPS,
  32 }
  33
  34 @article{ Clauss1998parametric,
  35     author = "Clauss, Philippe and Loechner, Vincent",
  36     title = "Parametric analysis of polyhedral iteration spaces",
  37     journal = "Journal of {VLSI} Signal Processing",
  38     publisher = "Kluwer Academic Publishers, Boston",
  39     year = "1998",
  40     volume = 19,
  41     pages = "179--194",
  42     number = 2,
  43     month = jul,
  44 }
  45
  46 @mastersthesis{ Seghir2002,
  47     title = {D\'enombrement des Point Entiers de l'Union et de
  48              l'Image des Poly\'edres Param\'etr\'es},
  49     author = "Rachid Seghir",
  50     month = jun,
  51     school = ICPS,
  52     year = 2002,
  53 }
  54
  55 @techreport{cdd,
  56     author = "K. Fukuda",
  57     title = "cdd.c: C-implementation of the double description method for computing all vertices and extremal rays of a convex polyhedron given by a system of linear inequalities",
  58     institution = "Department of Mathematics, Swiss Federal Institute of Technology, Lausanne, Switzerland",
  59    year =  1993,
  60     note = "program available from http://www.ifor.math.ethz.ch/~fukuda/fukuda.html",
  61 }
  62
  63 @PhdThesis{Loechner97phd,
  64     author = "V. Loechner",
  65     title = {Contribution \`a l'\'etude des poly\`edres
  66 param\'etr\'es et applications en parall\'elisation automatique},
  67     school = "University Louis Pasteur, Strasbourg",
  68     year =  1997,
  69 }
  70
  71 @PHDTHESIS{ Bik1996PhD,
  72   AUTHOR    = {A. J. C. Bik},
  73   TITLE     = {Compiler Support for Sparse Matrix Computations},
  74   SCHOOL    = {University of Leiden},
  75   ADDRESS   = {The Netherlands},
  76   YEAR      = {1996},
  77   ISBN      = {},
  78   NOTE      = {},
  79   CONTENTS  = {},
  80   sourceURL = {ftp://ftp.wi.leidenuniv.nl/pub/CS/PhDTheses/bik-96.ps.gz},
  81   FLAGS     = {own},
  82   TOPICS    = {Sparse Arrays}
  83 }
  84
  85 @PHDTHESIS{Verdoolaege2005PhD,
  86   AUTHOR = "Verdoolaege, Sven",
  87   TITLE = {Incremental Loop Transformations and Enumeration of Parametric Sets},
  88   SCHOOL = {Department of Computer Science, K.U.Leuven},
  89   YEAR = {2005},
  90   TYPE = {PHD},
  91   ADDRESS = {Leuven, Belgium},
  92   MONTH = apr,
  93 }
  94
  95 @misc{latte1.1,
  96     author = "De Loera, J. A. and Haws, D. and Hemmecke, R. and Huggins, P. and Tauzer, J. and Yoshida, R.",
  97     title = "A User's Guide for LattE v1.1",
  98     year = 2003,
  99     month = nov,
 100     note = {software package {\tt LattE} is available at {\tt http://www.math.ucdavis.edu/$\sim$latte/}},
 101 }
 102
 103 @misc{NTL,
 104     author = "Victor Shoup",
 105     title = "{NTL}",
 106     note = "Available from {\tt http://www.shoup.net/ntl/}",
 107     year = 2004,
 108 }
 109
 110 @incollection{polymake,
 111   author =       {Ewgenij Gawrilow and Michael Joswig},
 112   title =        {polymake: a Framework for Analyzing Convex Polytopes},
 113   pages =        {43-74},
 114   editor =       {Gil Kalai and G\"unter M. Ziegler},
 115   booktitle =    {Polytopes --- Combinatorics and Computation},
 116   publisher =    {Birkh\"auser},
 117   year =         {2000}
 118 }
 119
 120 @article{Stanley93monotonicity,
 121   author    = {Richard P. Stanley},
 122   title     = {A Monotonicity Property of h-vectors and h*-vectors.},
 123   journal   = {European Journal of Combinatorics},
 124   volume    = {14},
 125   number    = {3},
 126   year      = {1993},
 127   pages     = {251-258},
 128 }
 129
 130 @TechReport{ Omega_calc,
 131     author = "Wayne Kelly and Vadim Maslov and William Pugh and Evan Rosser and Tatiana Shpeisman and Dave Wonnacott",
 132     title = "The {Omega} Calculator and Library",
 133     month = nov,
 134     institution = "University of Maryland",
 135     year = 1996
 136 }
 137
 138 @TechReport{ Omega_lib,
 139     author = "Wayne Kelly and Vadim Maslov and William Pugh and Evan Rosser and Tatiana Shpeisman and Dave Wonnacott",
 140     title = "The {Omega} Library",
 141     month = nov,
 142     institution = "University of Maryland",
 143     year = 1996
 144 }
 145
 146 @inproceedings{Turjan2002,
 147     author = "Alexandru Turjan and Bart Kienhuis and Ed Deprettere",
 148     title = "A compile time based approach for solving out-of-order communication in {Kahn} Process Networks",
 149     booktitle = "IEEE 13th International Conference on Aplication-specific Systems, Architectures and Processors (ASAP'2002)",
 150     location = "San Jose, CA, USA",
 151     month = Jul,
 152     year =  2002
 153 }
 154
 155 @article{Loechner2002,
 156  author = {Vincent Loechner and Beno\^it Meister and Philippe Clauss},
 157  title = {Precise Data Locality Optimization of Nested Loops},
 158  journal = {J. Supercomput.},
 159  volume = {21},
 160  number = {1},
 161  year = {2002},
 162  issn = {0920-8542},
 163  pages = {37--76},
 164  doi = {http://dx.doi.org/10.1023/A:1013535431127},
 165  publisher = {Kluwer Academic Publishers},
 166  }
 167
 168 @inproceedings{Verdoolaege2004embedded,
 169   AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Seghir, Rachid and Loechner, Vincent",
 170   TITLE = {{A}nalytical computation of {E}hrhart polynomials and its applications for embedded systems},
 171   YEAR = {2004},
 172   booktitle = {2nd Workshop on Optimization for DSP and Embedded Systems, ODES-2},
 173   location = {Palo Alto, USA},
 174   month =  mar,
 175 }
 176
 177 @TECHREPORT{Verdoolaege2004TR,
 178   AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Seghir, Rachid and Loechner, Vincent",
 179   TITLE = {{A}nalytical computation of {E}hrhart polynomials and its applications for embedded systems},
 180   INSTITUTION = {Department of Computer Science, K.U.Leuven},
 181   YEAR = {2004},
 182   TYPE = {Report CW},
 183   NUMBER = {376},
 184   ADDRESS = {Leuven, Belgium},
 185   MONTH = {jan},
 186 NOTE = {URL = http://www.cs.kuleuven.ac.be/publicaties/rapporten/cw/CW376.abs.html},
 187 }
 188
 189 @TechReport{Seghir2004analytical,
 190         title = {Analytical Computation of {Ehrhart} Polynomials and its Application in Compile-Time Generated Cache Hints},
 191         author= {Rachid Seghir and Sven Verdoolaege and Kristof Beyls and Vincent Loechner},
 192         month = feb,
 193         year  = {2004},
 194         number = 118,
 195         institution = ICPS,
 196 }
 197
 198 @INPROCEEDINGS{Verdoolaege2004analytical,
 199   AUTHOR = "Verdoolaege, Sven and Seghir, Rachid and Beyls, Kristof and Loechner, Vincent and Bruynooghe, Maurice",
 200   TITLE = {{A}nalytical computation of {E}hrhart polynomials: {Enabling} more compiler analyses and optimizations},
 201   BOOKTITLE = {{P}roceedings of {I}nternational {C}onference on {C}ompilers, {A}rchitectures, and {S}ynthesis for {E}mbedded {S}ystems, {W}ashington {D}.{C}.},
 202   YEAR = {2004},
 203   pages = {248--258},
 204   month = sep,
 205 }
 206
 207 @TECHREPORT{Verdoolaege2004experiences,
 208   AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Catthoor, Francky",
 209   TITLE = {{E}xperiences with enumeration of integer projections of parametric polytopes},
 210   INSTITUTION = {K.U.Leuven, Department of Computer Science},
 211   YEAR = {2004},
 212   TYPE = {Report CW},
 213   NUMBER = {395},
 214   MONTH = oct,
 215 NOTE = {URL = http://www.cs.kuleuven.ac.be/publicaties/rapporten/cw/CW395.abs.html},
 216 }
 217
 218 @INPROCEEDINGS{Verdoolaege2005experiences,
 219   AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Catthoor, Francky",
 220   TITLE = {{E}xperiences with enumeration of integer projections of parametric polytopes},
 221   BOOKTITLE = {{P}roceedings of 14th {I}nternational {C}onference on {C}ompiler {C}onstruction, {E}dinburgh, {S}cotland},
 222   YEAR = {2005},
 223   EDITOR = {Bodik, R.},
 224   VOLUME = 3443,
 225     pages = "91-105",
 226     series = "Lecture Notes in Computer Science",
 227     publisher = "Springer-Verlag",
 228     address = "Berlin",
 229 }
 230
 231 @TECHREPORT{Verdoolaege2005barvinok,
 232   AUTHOR = "Verdoolaege, Sven and Woods, Kevin M. and Bruynooghe, Maurice and
 233 Cools, Ronald",
 234   YEAR = {2005},
 235   TITLE = {Computation and Manipulation of Enumerators of Integer Projections of
 236  Parametric Polytopes},
 237   TYPE = {Report CW},
 238   NUMBER = {392},
 239   INSTITUTION = {Dept.\ of Computer Science, K.U.Leuven},
 240   ADDRESS = {Leuven, Belgium},
 241 }
 242
 243 @misc{Verdoolaege2005couting,
 244     title = {{Counting with rational generating functions}},
 245     author = {Sven Verdoolaege and Kevin M. Woods},
 246     year = 2005,
 247     month = apr,
 248     eprint = {arXiv:math.CO/0504059}
 249 }
 250
 251 @article{Verdoolaege2007parametric,
 252     author = "S. Verdoolaege and R. Seghir and K. Beyls and V. Loechner and M. Bruynooghe",
 253     title = "Counting integer points in parametric polytopes using {Barvinok}'s rational functions",
 254     journal = "Algorithmica",
 255     year = 2007,
 256     note = "accepted for publication",
 257 }
 258
 259 @INPROCEEDINGS{Seghir2006memory,
 260   AUTHOR = "Rachid Seghir and Vincent Loechner",
 261   TITLE = {Memory Optimization by Counting Points in Integer Transformations of Parametric Polytopes},
 262   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},
 263   month = oct,
 264   YEAR = {2006}
 265 }
 266
 267 @article{Koeppe2006primal,
 268     title = {{A primal Barvinok algorithm based on irrational decompositions}},
 269     author = {Matthias K\"oppe},
 270   year =         2007,
 271   journal =      {SIAM Journal on Discrete Mathematics},
 272   volume = 21,
 273   number = 1,
 274   pages = {220--236},
 275   doi = {10.1137/060664768},
 276 }
 277
 278 @MISC{Beck2005Brion,
 279   author = {Matthias Beck and Christian Haase and Frank Sottile},
 280   title = {Theorems of {Brion}, {Lawrence}, and {Varchenko} on rational generating  functions for cones},
 281   url = {http://www.citebase.org/abstract?id=oai:arXiv.org:math/0506466},
 282   year = {2005}
 283 }
 284
 285 @article{Lasserre2005alternative,
 286     author = "Jean B. Lasserre and Eduardo S. Zeron",
 287     title = "An alternative algorithm for counting lattice points in a convex polytope",
 288     year = 2005,
 289     volume = 30,
 290     page = "597--614",
 291     journal = "Math. Oper. Res.",
 292 }
 293
 294 @article{Beyls2005hints,
 295 author= {Beyls, Kristof and  D'Hollander, Erik},
 296 title= {Generating Cache Hints for Improved Program Efficiency},
 297 journal= {Journal of Systems Architecture},
 298 year= {2005},
 299 month= {4},
 300 volume= {51},
 301 number= {4},
 302 pages= {223-250},
 303 publisher= {Elsevier},
 304 }
 305
 306 @TechReport{CFGV06,
 307   author       = {Clauss, P. and Fern\'andez, F. J. and Gabervetsky, D. and Verdoolaege, S.},
 308   title        = {Symbolic Polynomial Maximization over Convex Sets and its Application to Memory Requirement Estimation},
 309   institution  = {Universit\'e Louis Pasteur},
 310   number       = {06-04},
 311   month        = oct,
 312   year         = {2006},
 313   type         = {ICPS Research Report},
 314   url          = {http://icps.u-strasbg.fr/upload/icps-2006-173.pdf},
 315 }
 316
 317 @article{Cook1993implementation,
 318 AUTHOR={William Cook and Thomas Rutherford and Herbert E. Scarf and David F. Shallcross},
 319 TITLE={An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming},
 320 YEAR=1993,
 321 journal = "ORSA Journal on Computing",
 322 volume = 5,
 323 number = 2,
 324 }
 325
 326 @misc{GLPK,
 327 author = "Andrew Makhorin",
 328 title = "GNU Linear Programming Kit, Reference Manual, Version 4.11",
 329 year = 2006,
 330 month = jul,
 331 }
 332
 333 @inproceedings{Verdoolaege2006odes,
 334   AUTHOR = "Verdoolaege, Sven and Nikolov, Hristo and Stefanov, Todor",
 335   TITLE = {Improved Derivation of Process Networks},
 336   YEAR = {2006},
 337   booktitle = {4th Workshop on Optimization for DSP and Embedded Systems, ODES-4},
 338   location = {New York, USA},
 339   month =  mar,
 340 }
 341
 342 @article{Verdoolaege2007pn,
 343   AUTHOR = "Verdoolaege, Sven and Nikolov, Hristo and Stefanov, Todor",
 344   TITLE = {pn: A Tool for Improved Derivation of Process Networks},
 345   YEAR = {2007},
 346   volume = 2007,
 347   journal = "EURASIP Journal on Embedded Systems, special issue on
 348             Embedded Digital Signal Processing Systems",
 349   doi = {10.1155/2007/75947},
 350   publisher = "Hindawi Publishing Corporation",
 351 }
 352
 353 @article{Scarf2006Neighborhood,
 354   author    = {Herbert E. Scarf and
 355                Kevin M. Woods},
 356   title     = {Neighborhood Complexes and Generating Functions for Affine
 357                Semigroups.},
 358   journal   = {Discrete {\&} Computational Geometry},
 359   volume    = {35},
 360   number    = {3},
 361   year      = {2006},
 362   pages     = {385-403},
 363   ee        = {http://dx.doi.org/10.1007/s00454-005-1222-y},
 364   bibsource = {DBLP, http://dblp.uni-trier.de}
 365 }
 366
 367 @ARTICLE{Scarf1981indivisibilities:II,
 368 AUTHOR={Scarf, Herbert E},
 369 TITLE={Production Sets with Indivisibilities-Part {II}: The Case of Two Activities},
 370 JOURNAL={Econometrica},
 371 YEAR=1981,
 372 VOLUME={49},
 373 NUMBER={2},
 374 PAGES={395-423},
 375 MONTH=Mar,
 376 }
 377
 378 @phdthesis{Meister2004PhD,
 379     title = {Stating and Manipulating Periodicity in the Polytope Model. Applications to Program Analysis and Optimization},
 380     author= {Beno\^it Meister},
 381     institution = {Universit\'e Louis Pasteur},
 382     month = Dec,
 383     year  = {2004},
 384     school = ICPS,
 385 }
 386
 387 @article{Feautrier88parametric,
 388     author = "P. Feautrier",
 389     title = "Parametric Integer Programming",
 390     journal = "Operationnelle/Operations Research",
 391     volume = "22",
 392     number = "3",
 393     pages = "243--268",
 394     year = "1988",
 395     url = "citeseer.nj.nec.com/feautrier88parametric.html",
 396 }
 397
 398 @InProceedings{Gomory1963,
 399   author       = "R. E. Gomory",
 400   editor       = "R. L. Graves and P. Wolfe",
 401   booktitle    = "Recent Advances in Mathematical Programming",
 402   title        = "An algorithm for integer solutions to linear programming",
 403   publisher    = "McGraw-Hill",
 404   address      = "New York",
 405   pages        = "269--302",
 406   year         = "1963",
 407 }
 408
 409 @misc{Feautrier:PIP,
 410     author = "Paul Feautrier",
 411     title = "Solving Systems of Affine (In)Equalities: {PIP}'s User's Guide",
 412     year = 2006,
 413 }
 414
 415 @inproceedings{Barvinok1992volume,
 416  author = {Alexander I. Barvinok},
 417  title = {Computing the volume, counting integral points, and exponential sums},
 418  booktitle = {Proceedings of the eighth annual symposium on Computational geometry},
 419  year = {1992},
 420  isbn = {0-89791-517-8},
 421  pages = {161--170},
 422  location = {Berlin, Germany},
 423  doi = {http://doi.acm.org/10.1145/142675.142713},
 424  publisher = {ACM Press},
 425 }
 426
 427 @misc{Koeppe2006experiments,
 428     title = "Experiments with an algebraic scheme for estimating the number of lattice points in polyhedra",
 429     author = {De Loera, Jes\'us A. and Matthias K\"oppe},
 430     year = 2006,
 431     note = "Manuscript in preparation",
 432 }
 433
 434 @article{DeLoera2003effective,
 435     title = "Effective Lattice Point Counting in Rational Convex Polytopes",
 436     author = "De Loera, Jes\'us A. and Raymond Hemmecke and
 437               Jeremiah Tauzer and Ruriko Yoshida",
 438     year = 2004,
 439     journal = "The Journal of Symbolic Computation",
 440     volume = 38,
 441     number = 4,
 442     pages = "1273--1302",
 443     url = "http://www.math.ucdavis.edu/~latte/theory.html",
 444 }
 445
 446 @article{Barvinok1994,
 447     author = "A. I. Barvinok",
 448     title = "Computing the {Ehrhart} polynomial of a convex lattice polytope",
 449     journal = "Dicrete Comput. Geom.",
 450     volume =  12,
 451     year = 1994,
 452     pages = "35--48",
 453 }
 454
 455 @article {Brion88,
 456     AUTHOR = {Brion, Michel},
 457      TITLE = {Points entiers dans les poly\`edres convexes},
 458    JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
 459   FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
 460               Quatri\`eme S\'erie},
 461     VOLUME = {21},
 462       YEAR = {1988},
 463     NUMBER = {4},
 464      PAGES = {653--663},
 465       ISSN = {0012-9593},
 466      CODEN = {ASENAH},
 467    MRCLASS = {52A43 (11H06 12L10 14F12 32C40)},
 468   MRNUMBER = {90d:52020},
 469 MRREVIEWER = {Daniel Barlet},
 470 }
 471
 472 @misc{Koeppe2007parametric,
 473     title = {Computing parametric rational generating functions
 474   with a primal Barvinok algorithm},
 475     author = {Matthias K\"oppe and Sven Verdoolaege},
 476     year = 2007,
 477     note = "manuscript in preparation",
 478 }
 479
 480 @techreport{LLS06,
 481     author =       {D. Lepelley and A. Louichi and H. Smaoui},
 482     title =        {On {Ehrhart} Polynomials and Probability
 483                     Calculations in Voting Theory},
 484     institution =  {CERESUR / CREM},
 485     year =         {2006},
 486     type =         {Technical Report},
 487     number =       {200610},
 488     adress =      {Universit\'e de la R\'eunion},
 489     month =        Mar,
 490     howpublished = {available at \url{http://ideas.repec.org/p/tut/cremwp/200610.html}}
 491 }
 492
 493 @article{Barvinok2006simplex,
 494   author =       {Barvinok, Alexander I.},
 495   title =        {Computing the {Ehrhart} quasi-polynomial of a rational simplex},
 496   year =         2006,
 497   pages =        "1449-1466",
 498   volume =       75,
 499   journal =      "Math. Comp.",
 500   PUBLISHER = {American Mathematical Society},
 501 }
 502
 503 @mastersthesis{Rabl2006,
 504     title = "Volume Calculation and Estimation of Parameterized Integer Polytopes",
 505     author = "Tilmann Rabl",
 506     month = jan,
 507     school = Passau,
 508     year = 2006,
 509 }
 510
 511 @book{ Ehrhart1977,
 512     author = "E. Ehrhart",
 513     title = "Polyn\^omes arithm\'etiques et M\'ethode des Poly\`edres en Combinatoire",
 514     series = "International Series of Numerical Mathematics",
 515     volume = 35,
 516     publisher = "Birkhauser Verlag",
 517     address =  "Basel/Stuttgart",
 518     year = 1977,
 519 }
 520
 521 @book{Stanley1986,
 522     author =       "Richard P. Stanley",
 523     title =        "Enumerative Combinatorics",
 524     volume =     1,
 525     publisher =    "Cambridge University Press",
 526     year = 1986,
 527 }
 528
 529 @misc{Woods2006personal,
 530     author = "Kevin M. Woods",
 531     title = "personal communication",
 532     year = 2006,
 533     month = jun,
 534 }
 535
 536 @Techreport{Pop06,
 537   Author = "S. Pop and G.-A. Silber and A. Cohen and C. Bastoul
 538             and S. Girbal and N. Vasilache",
 539   Title = "{GRAPHITE}: Polyhedral Analyses and Optimizations for {GCC}",
 540   Number = "A/378/CRI",
 541   Institution = "Centre de Recherche en Informatique,
 542                  \'Ecole des Mines de Paris",
 543   Address = "Fontainebleau, France",
 544   Year = 2006,
 545   Note = "Contribution to the GNU Compilers Collection Developers Summit 2006
 546           (GCC Summit 06), Ottawa, Canada, June 28--30, 2006",
 547   Abstract = "We present a plan to add loop nest optimizations in GCC
 548               based on polyhedral representations of loop nests. We
 549               advocate a static analysis approach based on a hierarchy
 550               of interchangeable abstractions with solvers that range
 551               from the exact solvers such as OMEGA, to faster but less
 552               precise solvers based on more coarse abstractions. The
 553               intermediate representation GRAPHITE (GIMPLE Represented
 554               as Polyhedra with Interchangeable Envelopes), built on
 555               GIMPLE and the natural loops, hosts the high level loop
 556               transformations. We base this presentation on the
 557               WRaP-IT project developed in the Alchemy group at INRIA
 558               Futurs and Paris-Sud University, on the PIPS compiler
 559               developed at \'Ecole des mines de Paris, and on a joint
 560               work with several members of the static analysis and
 561               polyhedral compilation community in France.
 562
 563               The main goal of this project is to bring more high
 564               level loop optimizations to GCC: loop fusion, tiling,
 565               strip mining, etc. Thanks to the WRaP-IT experience, we
 566               know that the polyhedral analyzes and transformations
 567               are affordable in a production compiler. A second goal
 568               of this project is to experiment with compile time
 569               reduction versus attainable precision when replacing
 570               operations on polyhedra with faster operations on more
 571               abstract domains. However, the use of a too coarse
 572               representation for computing might also result in an
 573               over approximated solution that cannot be used in
 574               subsequent computations. There exists a trade off
 575               between speed of the computation and the attainable
 576               precision that has not yet been analyzed for real world
 577               programs."
 578 }
 579
 580 @article{Baldoni2006,
 581   author    = {Baldoni-Silva, M. Welleda and
 582                Matthias Beck and
 583                Charles Cochet and
 584                Mich{\`e}le Vergne},
 585   title     = {Volume Computation for Polytopes and Partition Functions
 586                for Classical Root Systems.},
 587   journal   = {Discrete {\&} Computational Geometry},
 588   volume    = {35},
 589   number    = {4},
 590   year      = {2006},
 591   pages     = {551-595},
 592   ee        = {http://dx.doi.org/10.1007/s00454-006-1234-2},
 593   bibsource = {DBLP, http://dblp.uni-trier.de}
 594 }
 595
 596 @MISC{Meister2007b,
 597   author = {Beno\^it Meister and Sven Verdoolaege},
 598   title = {Approximating the Number of Integer Points in Parametric Polytopes
 599          by Polynomials},
 600   year = {2007},
 601   note = {manuscript in preparation},
 602 }
 603
 604 @misc{Devos2007,
 605     title = "Bounds on Quasi-Polynomials for Static Program Analysis",
 606     author = {Harald Devos and Sven Verdoolaege and Van Campenhout, Jan and
 607               Dirk Stroobandt},
 608     year = 2007,
 609     note = "manuscript in preparation",
 610 }
 611
 612 @article{Bueler2000exact,
 613     booktitle = "Polytopes --- Combinatorics and Computation",
 614     editor = "G. Kalai and G. Ziegler",
 615     publisher = {Birkh\"auser-Verlag},
 616     note = "DMV Seminar Band 29",
 617     title = "Exact volume computation for polytopes: A practical study",
 618     year = 2000,
 619     author = {Benno B\"ueler and Andreas Enge and Komei Fukuda},
 620 }
 621
 622 @article{Cohen1979volumes,
 623  author = {Jacques Cohen and Timothy Hickey},
 624  title = {Two Algorithms for Determining Volumes of Convex Polyhedra},
 625  journal = {J. ACM},
 626  volume = {26},
 627  number = {3},
 628  year = {1979},
 629  issn = {0004-5411},
 630  pages = {401--414},
 631  doi = {http://doi.acm.org/10.1145/322139.322141},
 632  publisher = {ACM Press},
 633  address = {New York, NY, USA},
 634 }
 635
 636 @article{Lee1991,
 637     author = "C. W. Lee",
 638     title = "Regular triangulations of convex polytopes",
 639     journal =  "Applied Geometry and Discrete Mathematics --- The Victor Klee Festschrift",
 640     editor = "P. Gritzmann and B. Sturmfels",
 641     series = "DIMACS series in Discrete Math. and Theoretical Comp. Science, 4",
 642     year = 1991,
 643     pages = "443--456",
 644     volume = 4,
 645 }
 646
 647 @PhDThesis{ DeLoera1995,
 648     author = "De Loera, J. A.",
 649     title = "Triangulations of Polytopes and Computational Algebra",
 650     school = "Cornell University",
 651     month =  May,
 652     year = 1995,
 653 }
 654
 655 @book{Henrici1974,
 656     series = "Pure and applied mathematics",
 657     AUTHOR = {Henrici, Peter},
 658      TITLE = {Applied and Computational Complex Analysis},
 659       NOTE = {Volume 1: Power series---integration---conformal
 660               mapping---location of zeros,
 661               Pure and Applied Mathematics},
 662  PUBLISHER = {Wiley-Interscience [John Wiley \& Sons]},
 663    ADDRESS = {New York},
 664       YEAR = {1974},
 665      PAGES = {xv+682},
 666    MRCLASS = {30-02 (65E05)},
 667   MRNUMBER = {MR0372162 (51 \#8378)},
 668 MRREVIEWER = {M. Marden},
 669 }
 670
 671 @article{Barvinok1999,
 672     author = "A. Barvinok and J. Pommersheim",
 673     title = "An algorithmic theory of lattice points in polyhedra",
 674     journal = "New Perspectives in Algebraic Combinatorics",
 675     series = "MSRI book series",
 676     volume =  "38",
 677     pages = "91--147",
 678     publisher = "Cambridge University Press, Cambridge",
 679     year = 1999,
 680 }
 681
 682 @Misc{latte-macchiato,
 683   author =       {K{\"o}ppe, Matthias},
 684   title =        {{LattE macchiato}, version 1.2-mk-0.7.1, an improved version of {De Loera}
 685                   et al.'s {LattE} program for counting integer points in
 686                   polyhedra with variants of {Barvinok}'s algorithm},
 687   howpublished = {Available from URL {\url{http://www.math.uni-magdeburg.de/~mkoeppe/latte/}}}
 688 ,
 689   year = 2006
 690 }
 691
 692 @inproceedings{Tawbi1994,
 693     author = "N. Tawbi",
 694     title = "Estimation of Nested Loops execution time by Integer Arithmetic in Convex Polyhedra",
 695     booktitle = "Proceedings of the 8th International Parallel Processing Symposium",
 696     publisher = "IEEE Computer Society Press",
 697     pages =  "217--221",
 698     year = 1994,
 699 }
 700
 701 @inproceedings{Sakellariou1997sums,
 702     author = "Rizos Sakellariou",
 703     title = "Symbolic Evaluation of Sums for Parallelising Compilers",
 704     editor = "A. Sydow",
 705     booktitle = "Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics",
 706     location = "Berlin",
 707     month = Aug,
 708     year = 1997,
 709     volume = 2,
 710     series = "Wissenschaft \& Technik Verlag",
 711     pages = "685-690",
 712 }
 713
 714 @article{VanEngelen2004,
 715  author =       {Van Engelen, R. A. and K. Gallivan and B. Walsh},
 716  title =        {Parametric Timing Estimation With the {N}ewton-{G}regory Formulae},
 717  journal =      {Journal of Concurrency and Computation: Practice and Experience},
 718  volume =       {18},
 719  number =       {10},
 720  year =         {2006},
 721  month =        sep,
 722  issn =         {},
 723  pages =        {1434--1464},
 724  publisher =    {Wiley Press, USA},
 725 }