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{Verdoolaege2007counting,
 244     title = {{Counting with rational generating functions}},
 245     author = {Sven Verdoolaege and Kevin M. Woods},
 246     year = 2007,
 247     eprint = {arXiv:math.CO/0504059},
 248     note = "To appear in The Journal of Symbolic Computation",
 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     volume = 48,
 257     number = 1,
 258     month = jun,
 259     publisher = "Springer New York",
 260     pages = "37--66",
 261 }
 262
 263 @INPROCEEDINGS{Seghir2006memory,
 264   AUTHOR = "Rachid Seghir and Vincent Loechner",
 265   TITLE = {Memory Optimization by Counting Points in Integer Transformations of Parametric Polytopes},
 266   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},
 267   month = oct,
 268   YEAR = {2006}
 269 }
 270
 271 @article{Koeppe2006primal,
 272     title = {{A primal Barvinok algorithm based on irrational decompositions}},
 273     author = {Matthias K\"oppe},
 274   year =         2007,
 275   journal =      {SIAM Journal on Discrete Mathematics},
 276   volume = 21,
 277   number = 1,
 278   pages = {220--236},
 279   doi = {10.1137/060664768},
 280 }
 281
 282 @MISC{Beck2005Brion,
 283   author = {Matthias Beck and Christian Haase and Frank Sottile},
 284   title = {Theorems of {Brion}, {Lawrence}, and {Varchenko} on rational generating  functions for cones},
 285   url = {http://www.citebase.org/abstract?id=oai:arXiv.org:math/0506466},
 286   year = {2005}
 287 }
 288
 289 @article{Lasserre2005alternative,
 290     author = "Jean B. Lasserre and Eduardo S. Zeron",
 291     title = "An alternative algorithm for counting lattice points in a convex polytope",
 292     year = 2005,
 293     volume = 30,
 294     page = "597--614",
 295     journal = "Math. Oper. Res.",
 296 }
 297
 298 @article{Beyls2005hints,
 299 author= {Beyls, Kristof and  D'Hollander, Erik},
 300 title= {Generating Cache Hints for Improved Program Efficiency},
 301 journal= {Journal of Systems Architecture},
 302 year= {2005},
 303 month= {4},
 304 volume= {51},
 305 number= {4},
 306 pages= {223-250},
 307 publisher= {Elsevier},
 308 }
 309
 310 @TechReport{CFGV06,
 311   author       = {Clauss, P. and Fern\'andez, F. J. and Gabervetsky, D. and Verdoolaege, S.},
 312   title        = {Symbolic Polynomial Maximization over Convex Sets and its Application to Memory Requirement Estimation},
 313   institution  = {Universit\'e Louis Pasteur},
 314   number       = {06-04},
 315   month        = oct,
 316   year         = {2006},
 317   type         = {ICPS Research Report},
 318   url          = {http://icps.u-strasbg.fr/upload/icps-2006-173.pdf},
 319 }
 320
 321 @article{Cook1993implementation,
 322 AUTHOR={William Cook and Thomas Rutherford and Herbert E. Scarf and David F. Shallcross},
 323 TITLE={An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming},
 324 YEAR=1993,
 325 journal = "ORSA Journal on Computing",
 326 volume = 5,
 327 number = 2,
 328 }
 329
 330 @misc{GLPK,
 331 author = "Andrew Makhorin",
 332 title = "GNU Linear Programming Kit, Reference Manual, Version 4.11",
 333 year = 2006,
 334 month = jul,
 335 }
 336
 337 @inproceedings{Verdoolaege2006odes,
 338   AUTHOR = "Verdoolaege, Sven and Nikolov, Hristo and Stefanov, Todor",
 339   TITLE = {Improved Derivation of Process Networks},
 340   YEAR = {2006},
 341   booktitle = {4th Workshop on Optimization for DSP and Embedded Systems, ODES-4},
 342   location = {New York, USA},
 343   month =  mar,
 344 }
 345
 346 @article{Verdoolaege2007pn,
 347   AUTHOR = "Verdoolaege, Sven and Nikolov, Hristo and Stefanov, Todor",
 348   TITLE = {pn: A Tool for Improved Derivation of Process Networks},
 349   YEAR = {2007},
 350   volume = 2007,
 351   journal = "EURASIP Journal on Embedded Systems, special issue on
 352             Embedded Digital Signal Processing Systems",
 353   doi = {10.1155/2007/75947},
 354   publisher = "Hindawi Publishing Corporation",
 355 }
 356
 357 @article{Scarf2006Neighborhood,
 358   author    = {Herbert E. Scarf and
 359                Kevin M. Woods},
 360   title     = {Neighborhood Complexes and Generating Functions for Affine
 361                Semigroups.},
 362   journal   = {Discrete {\&} Computational Geometry},
 363   volume    = {35},
 364   number    = {3},
 365   year      = {2006},
 366   pages     = {385-403},
 367   ee        = {http://dx.doi.org/10.1007/s00454-005-1222-y},
 368   bibsource = {DBLP, http://dblp.uni-trier.de}
 369 }
 370
 371 @ARTICLE{Scarf1981indivisibilities:II,
 372 AUTHOR={Scarf, Herbert E},
 373 TITLE={Production Sets with Indivisibilities-Part {II}: The Case of Two Activities},
 374 JOURNAL={Econometrica},
 375 YEAR=1981,
 376 VOLUME={49},
 377 NUMBER={2},
 378 PAGES={395-423},
 379 MONTH=Mar,
 380 }
 381
 382 @phdthesis{Meister2004PhD,
 383     title = {Stating and Manipulating Periodicity in the Polytope Model. Applications to Program Analysis and Optimization},
 384     author= {Beno\^it Meister},
 385     institution = {Universit\'e Louis Pasteur},
 386     month = Dec,
 387     year  = {2004},
 388     school = ICPS,
 389 }
 390
 391 @article{Feautrier88parametric,
 392     author = "P. Feautrier",
 393     title = "Parametric Integer Programming",
 394     journal = "Operationnelle/Operations Research",
 395     volume = "22",
 396     number = "3",
 397     pages = "243--268",
 398     year = "1988",
 399     url = "citeseer.nj.nec.com/feautrier88parametric.html",
 400 }
 401
 402 @InProceedings{Gomory1963,
 403   author       = "R. E. Gomory",
 404   editor       = "R. L. Graves and P. Wolfe",
 405   booktitle    = "Recent Advances in Mathematical Programming",
 406   title        = "An algorithm for integer solutions to linear programming",
 407   publisher    = "McGraw-Hill",
 408   address      = "New York",
 409   pages        = "269--302",
 410   year         = "1963",
 411 }
 412
 413 @misc{Feautrier:PIP,
 414     author = "Paul Feautrier",
 415     title = "Solving Systems of Affine (In)Equalities: {PIP}'s User's Guide",
 416     year = 2006,
 417 }
 418
 419 @inproceedings{Barvinok1992volume,
 420  author = {Alexander I. Barvinok},
 421  title = {Computing the volume, counting integral points, and exponential sums},
 422  booktitle = {Proceedings of the eighth annual symposium on Computational geometry},
 423  year = {1992},
 424  isbn = {0-89791-517-8},
 425  pages = {161--170},
 426  location = {Berlin, Germany},
 427  doi = {http://doi.acm.org/10.1145/142675.142713},
 428  publisher = {ACM Press},
 429 }
 430
 431 @misc{Koeppe2006experiments,
 432     title = "Experiments with an algebraic scheme for estimating the number of lattice points in polyhedra",
 433     author = {De Loera, Jes\'us A. and Matthias K\"oppe},
 434     year = 2006,
 435     note = "Manuscript in preparation",
 436 }
 437
 438 @article{DeLoera2003effective,
 439     title = "Effective Lattice Point Counting in Rational Convex Polytopes",
 440     author = "De Loera, Jes\'us A. and Raymond Hemmecke and
 441               Jeremiah Tauzer and Ruriko Yoshida",
 442     year = 2004,
 443     journal = "The Journal of Symbolic Computation",
 444     volume = 38,
 445     number = 4,
 446     pages = "1273--1302",
 447     url = "http://www.math.ucdavis.edu/~latte/theory.html",
 448 }
 449
 450 @article{Barvinok1994,
 451     author = "A. I. Barvinok",
 452     title = "Computing the {Ehrhart} polynomial of a convex lattice polytope",
 453     journal = "Dicrete Comput. Geom.",
 454     volume =  12,
 455     year = 1994,
 456     pages = "35--48",
 457 }
 458
 459 @article {Brion88,
 460     AUTHOR = {Brion, Michel},
 461      TITLE = {Points entiers dans les poly\`edres convexes},
 462    JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
 463   FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
 464               Quatri\`eme S\'erie},
 465     VOLUME = {21},
 466       YEAR = {1988},
 467     NUMBER = {4},
 468      PAGES = {653--663},
 469       ISSN = {0012-9593},
 470      CODEN = {ASENAH},
 471    MRCLASS = {52A43 (11H06 12L10 14F12 32C40)},
 472   MRNUMBER = {90d:52020},
 473 MRREVIEWER = {Daniel Barlet},
 474 }
 475
 476 @misc{Koeppe2007parametric,
 477     title = {Computing parametric rational generating functions
 478   with a primal Barvinok algorithm},
 479     author = {Matthias K\"oppe and Sven Verdoolaege},
 480     year = 2007,
 481     note = "manuscript in preparation",
 482 }
 483
 484 @article{Lepelley2007,
 485     author =       {Dominique Lepelley and Ahmed Louichi and Hatem Smaoui},
 486     title =        {On {Ehrhart} Polynomials and Probability
 487                     Calculations in Voting Theory},
 488     journal =      "Social Choice and Welfare",
 489     year =         {2007},
 490     month =        Apr,
 491     Publisher =    "Springer Berlin / Heidelberg",
 492     ISSN =         "0176-1714 (Print) 1432-217X (Online)",
 493     DOI =           "10.1007/s00355-007-0236-1",
 494 }
 495
 496 @article{Barvinok2006simplex,
 497   author =       {Barvinok, Alexander I.},
 498   title =        {Computing the {Ehrhart} quasi-polynomial of a rational simplex},
 499   year =         2006,
 500   pages =        "1449-1466",
 501   volume =       75,
 502   journal =      "Math. Comp.",
 503   PUBLISHER = {American Mathematical Society},
 504 }
 505
 506 @mastersthesis{Rabl2006,
 507     title = "Volume Calculation and Estimation of Parameterized Integer Polytopes",
 508     author = "Tilmann Rabl",
 509     month = jan,
 510     school = Passau,
 511     year = 2006,
 512 }
 513
 514 @book{ Ehrhart1977,
 515     author = "E. Ehrhart",
 516     title = "Polyn\^omes arithm\'etiques et M\'ethode des Poly\`edres en Combinatoire",
 517     series = "International Series of Numerical Mathematics",
 518     volume = 35,
 519     publisher = "Birkhauser Verlag",
 520     address =  "Basel/Stuttgart",
 521     year = 1977,
 522 }
 523
 524 @book{Stanley1986,
 525     author =       "Richard P. Stanley",
 526     title =        "Enumerative Combinatorics",
 527     volume =     1,
 528     publisher =    "Cambridge University Press",
 529     year = 1986,
 530 }
 531
 532 @misc{Woods2006personal,
 533     author = "Kevin M. Woods",
 534     title = "personal communication",
 535     year = 2006,
 536     month = jun,
 537 }
 538
 539 @Techreport{Pop06,
 540   Author = "S. Pop and G.-A. Silber and A. Cohen and C. Bastoul
 541             and S. Girbal and N. Vasilache",
 542   Title = "{GRAPHITE}: Polyhedral Analyses and Optimizations for {GCC}",
 543   Number = "A/378/CRI",
 544   Institution = "Centre de Recherche en Informatique,
 545                  \'Ecole des Mines de Paris",
 546   Address = "Fontainebleau, France",
 547   Year = 2006,
 548   Note = "Contribution to the GNU Compilers Collection Developers Summit 2006
 549           (GCC Summit 06), Ottawa, Canada, June 28--30, 2006",
 550   Abstract = "We present a plan to add loop nest optimizations in GCC
 551               based on polyhedral representations of loop nests. We
 552               advocate a static analysis approach based on a hierarchy
 553               of interchangeable abstractions with solvers that range
 554               from the exact solvers such as OMEGA, to faster but less
 555               precise solvers based on more coarse abstractions. The
 556               intermediate representation GRAPHITE (GIMPLE Represented
 557               as Polyhedra with Interchangeable Envelopes), built on
 558               GIMPLE and the natural loops, hosts the high level loop
 559               transformations. We base this presentation on the
 560               WRaP-IT project developed in the Alchemy group at INRIA
 561               Futurs and Paris-Sud University, on the PIPS compiler
 562               developed at \'Ecole des mines de Paris, and on a joint
 563               work with several members of the static analysis and
 564               polyhedral compilation community in France.
 565
 566               The main goal of this project is to bring more high
 567               level loop optimizations to GCC: loop fusion, tiling,
 568               strip mining, etc. Thanks to the WRaP-IT experience, we
 569               know that the polyhedral analyzes and transformations
 570               are affordable in a production compiler. A second goal
 571               of this project is to experiment with compile time
 572               reduction versus attainable precision when replacing
 573               operations on polyhedra with faster operations on more
 574               abstract domains. However, the use of a too coarse
 575               representation for computing might also result in an
 576               over approximated solution that cannot be used in
 577               subsequent computations. There exists a trade off
 578               between speed of the computation and the attainable
 579               precision that has not yet been analyzed for real world
 580               programs."
 581 }
 582
 583 @article{Baldoni2006,
 584   author    = {Baldoni-Silva, M. Welleda and
 585                Matthias Beck and
 586                Charles Cochet and
 587                Mich{\`e}le Vergne},
 588   title     = {Volume Computation for Polytopes and Partition Functions
 589                for Classical Root Systems.},
 590   journal   = {Discrete {\&} Computational Geometry},
 591   volume    = {35},
 592   number    = {4},
 593   year      = {2006},
 594   pages     = {551-595},
 595   ee        = {http://dx.doi.org/10.1007/s00454-006-1234-2},
 596   bibsource = {DBLP, http://dblp.uni-trier.de}
 597 }
 598
 599 @MISC{Meister2007b,
 600   author = {Beno\^it Meister and Sven Verdoolaege},
 601   title = {Approximating the Number of Integer Points in Parametric Polytopes
 602          by Polynomials},
 603   year = {2007},
 604   note = {manuscript in preparation},
 605 }
 606
 607 @misc{Devos2007,
 608     title = "Bounds on Quasi-Polynomials for Static Program Analysis",
 609     author = {Harald Devos and Sven Verdoolaege and Van Campenhout, Jan and
 610               Dirk Stroobandt},
 611     year = 2007,
 612     note = "manuscript in preparation",
 613 }
 614
 615 @article{Bueler2000exact,
 616     booktitle = "Polytopes --- Combinatorics and Computation",
 617     editor = "G. Kalai and G. Ziegler",
 618     publisher = {Birkh\"auser-Verlag},
 619     note = "DMV Seminar Band 29",
 620     title = "Exact volume computation for polytopes: A practical study",
 621     year = 2000,
 622     author = {Benno B\"ueler and Andreas Enge and Komei Fukuda},
 623 }
 624
 625 @article{Cohen1979volumes,
 626  author = {Jacques Cohen and Timothy Hickey},
 627  title = {Two Algorithms for Determining Volumes of Convex Polyhedra},
 628  journal = {J. ACM},
 629  volume = {26},
 630  number = {3},
 631  year = {1979},
 632  issn = {0004-5411},
 633  pages = {401--414},
 634  doi = {http://doi.acm.org/10.1145/322139.322141},
 635  publisher = {ACM Press},
 636  address = {New York, NY, USA},
 637 }
 638
 639 @article{Lee1991,
 640     author = "C. W. Lee",
 641     title = "Regular triangulations of convex polytopes",
 642     journal =  "Applied Geometry and Discrete Mathematics --- The Victor Klee Festschrift",
 643     editor = "P. Gritzmann and B. Sturmfels",
 644     series = "DIMACS series in Discrete Math. and Theoretical Comp. Science, 4",
 645     year = 1991,
 646     pages = "443--456",
 647     volume = 4,
 648 }
 649
 650 @PhDThesis{ DeLoera1995,
 651     author = "De Loera, J. A.",
 652     title = "Triangulations of Polytopes and Computational Algebra",
 653     school = "Cornell University",
 654     month =  May,
 655     year = 1995,
 656 }
 657
 658 @book{Henrici1974,
 659     series = "Pure and applied mathematics",
 660     AUTHOR = {Henrici, Peter},
 661      TITLE = {Applied and Computational Complex Analysis},
 662       NOTE = {Volume 1: Power series---integration---conformal
 663               mapping---location of zeros,
 664               Pure and Applied Mathematics},
 665  PUBLISHER = {Wiley-Interscience [John Wiley \& Sons]},
 666    ADDRESS = {New York},
 667       YEAR = {1974},
 668      PAGES = {xv+682},
 669    MRCLASS = {30-02 (65E05)},
 670   MRNUMBER = {MR0372162 (51 \#8378)},
 671 MRREVIEWER = {M. Marden},
 672 }
 673
 674 @article{Barvinok1999,
 675     author = "A. I. Barvinok and J. Pommersheim",
 676     title = "An algorithmic theory of lattice points in polyhedra",
 677     journal = "New Perspectives in Algebraic Combinatorics",
 678     series = "MSRI book series",
 679     volume =  "38",
 680     pages = "91--147",
 681     publisher = "Cambridge University Press, Cambridge",
 682     year = 1999,
 683 }
 684
 685 @Misc{latte-macchiato,
 686   author =       {K\"oppe, Matthias},
 687   title =        {{LattE macchiato}, version 1.2-mk-0.7.1, an improved version of {De Loera}
 688                   et al.'s {LattE} program for counting integer points in
 689                   polyhedra with variants of {Barvinok}'s algorithm},
 690   howpublished = {Available from URL {\url{http://www.math.uni-magdeburg.de/~mkoeppe/latte/}}}
 691 ,
 692   year = 2006
 693 }
 694
 695 @inproceedings{Tawbi1994,
 696     author = "N. Tawbi",
 697     title = "Estimation of Nested Loops execution time by Integer Arithmetic in Convex Polyhedra",
 698     booktitle = "Proceedings of the 8th International Parallel Processing Symposium",
 699     publisher = "IEEE Computer Society Press",
 700     pages =  "217--221",
 701     year = 1994,
 702 }
 703
 704 @inproceedings{Sakellariou1997sums,
 705     author = "Rizos Sakellariou",
 706     title = "Symbolic Evaluation of Sums for Parallelising Compilers",
 707     editor = "A. Sydow",
 708     booktitle = "Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics",
 709     location = "Berlin",
 710     month = Aug,
 711     year = 1997,
 712     volume = 2,
 713     series = "Wissenschaft \& Technik Verlag",
 714     pages = "685-690",
 715 }
 716
 717 @article{VanEngelen2004,
 718  author =       {Van Engelen, R. A. and K. Gallivan and B. Walsh},
 719  title =        {Parametric Timing Estimation With the {N}ewton-{G}regory Formulae},
 720  journal =      {Journal of Concurrency and Computation: Practice and Experience},
 721  volume =       {18},
 722  number =       {10},
 723  year =         {2006},
 724  month =        sep,
 725  issn =         {},
 726  pages =        {1434--1464},
 727  publisher =    {Wiley Press, USA},
 728 }
 729
 730 @misc{Berline2006local,
 731     title = "Local Euler-Maclaurin formula for polytopes",
 732     author = "Nicole Berline and Mich\`ele Vergne",
 733     year = 2006,
 734     month = jul,
 735     note = "http://arXiv.org/abs/math/0507256",
 736 }
 737
 738 @misc{Berline2007personal,
 739     author = "Nicole Berline",
 740     title = "personal communication",
 741     year = 2007,
 742     month = aug,
 743 }
 744
 745 @inproceedings{Eisenschmidt2007integrally,
 746         author = {Eisenschmidt, Elke and K\"oppe, Matthias},
 747         title = "Integrally  indecomposable polytopes and the survivable network design problem",
 748         note = "To appear",
 749         booktitle = "Electronic proceedings of the 6th International Workshop on the Design of Reliable Communication Networks, DRCN 2007",
 750         locationg = "La Rochelle, France",
 751         year = 2007,
 752 }
 753
 754 @inproceedings{Pfeifle2003,
 755   author    = {Julian Pfeifle and
 756                J{\"o}rg Rambau},
 757   title     = {Computing Triangulations Using Oriented Matroids.},
 758   booktitle = {Algebra, Geometry, and Software Systems},
 759   year      = {2003},
 760   publisher = {Springer},
 761   pages     = {49-75},
 762   editor    = {Michael Joswig and
 763                Nobuki Takayama},
 764 }
 765
 766 @book{Gelfand1994,
 767     author = "I. M. Gelfand and Mikhail Kapranov and A. V. Zelevinsky",
 768     title = "Discriminants, Resultants and Multidimensional Determinants",
 769     publisher = "Birkhauser, Boston",
 770     year = 1994,
 771 }