doc/barvinok.bib

   1 @string(ICPS = "ICPS, Universit\'e Louis Pasteur de Strasbourg, France")
   2 @string(Passau = {Universit\"at Passau})
   3
   4 @techreport{ Wilde1993,
   5     author = "D. K. Wilde",
   6     title = "A Library for doing polyhedral operations",
   7     number = "785",
   8     institution = "IRISA, Rennes, France",
   9     pages = "45 p.",
  10     year = 1993,
  11     url = "citeseer.nj.nec.com/article/wilde93library.html",
  12     note = "\\http://www.irisa.fr/EXTERNE/bibli/pi/pi785.html"
  13 }
  14
  15 @article{ Loechner97parameterized,
  16     author = "Vincent Loechner and Doran K. Wilde",
  17     title = "Parameterized Polyhedra and Their Vertices",
  18     journal = "International Journal of Parallel Programming",
  19     volume = "25",
  20     number = "6",
  21     pages = "525--549",
  22     year = "1997",
  23     month = dec,
  24     publisher = {Kluwer Academic Publishers},
  25     url = "citeseer.nj.nec.com/article/loechner95parameterized.html" }
  26
  27 @TechReport{ Loechner1999,
  28     author = "Vincent Loechner",
  29     month = mar,
  30     year = 1999,
  31     title = "PolyLib: A Library for Manipulating Parameterized Polyhedra",
  32     institution = ICPS,
  33 }
  34
  35 @article{ Clauss1998parametric,
  36     author = "Clauss, Philippe and Loechner, Vincent",
  37     title = "Parametric analysis of polyhedral iteration spaces",
  38     journal = "Journal of {VLSI} Signal Processing",
  39     publisher = "Kluwer Academic Publishers, Boston",
  40     year = "1998",
  41     volume = 19,
  42     pages = "179--194",
  43     number = 2,
  44     month = jul,
  45 }
  46
  47 @mastersthesis{ Seghir2002,
  48     title = {D\'enombrement des Point Entiers de l'Union et de
  49              l'Image des Poly\'edres Param\'etr\'es},
  50     author = "Rachid Seghir",
  51     month = jun,
  52     school = ICPS,
  53     year = 2002,
  54 }
  55
  56 @techreport{cdd,
  57     author = "K. Fukuda",
  58     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",
  59     institution = "Department of Mathematics, Swiss Federal Institute of Technology, Lausanne, Switzerland",
  60    year =  1993,
  61     note = "program available from http://www.ifor.math.ethz.ch/~fukuda/fukuda.html",
  62 }
  63
  64 @PhdThesis{Loechner97phd,
  65     author = "V. Loechner",
  66     title = {Contribution \`a l'\'etude des poly\`edres
  67 param\'etr\'es et applications en parall\'elisation automatique},
  68     school = "University Louis Pasteur, Strasbourg",
  69     year =  1997,
  70 }
  71
  72 @PHDTHESIS{ Bik1996PhD,
  73   AUTHOR    = {A. J. C. Bik},
  74   TITLE     = {Compiler Support for Sparse Matrix Computations},
  75   SCHOOL    = {University of Leiden},
  76   ADDRESS   = {The Netherlands},
  77   YEAR      = {1996},
  78   ISBN      = {},
  79   NOTE      = {},
  80   CONTENTS  = {},
  81   sourceURL = {ftp://ftp.wi.leidenuniv.nl/pub/CS/PhDTheses/bik-96.ps.gz},
  82   FLAGS     = {own},
  83   TOPICS    = {Sparse Arrays}
  84 }
  85
  86 @PHDTHESIS{Verdoolaege2005PhD,
  87   AUTHOR = "Verdoolaege, Sven",
  88   TITLE = {Incremental Loop Transformations and Enumeration of Parametric Sets},
  89   SCHOOL = {Department of Computer Science, K.U.Leuven},
  90   YEAR = {2005},
  91   TYPE = {PHD},
  92   ADDRESS = {Leuven, Belgium},
  93   MONTH = apr,
  94 }
  95
  96 @misc{latte1.1,
  97     author = "De Loera, J. A. and Haws, D. and Hemmecke, R. and Huggins, P. and Tauzer, J. and Yoshida, R.",
  98     title = "A User's Guide for LattE v1.1",
  99     year = 2003,
 100     month = nov,
 101     note = {software package {\tt LattE} is available at {\tt http://www.math.ucdavis.edu/$\sim$latte/}},
 102 }
 103
 104 @misc{NTL,
 105     author = "Victor Shoup",
 106     title = "{NTL}",
 107     note = "Available from {\tt http://www.shoup.net/ntl/}",
 108     year = 2004,
 109 }
 110
 111 @incollection{polymake,
 112   author =       {Ewgenij Gawrilow and Michael Joswig},
 113   title =        {polymake: a Framework for Analyzing Convex Polytopes},
 114   pages =        {43-74},
 115   editor =       {Gil Kalai and G\"unter M. Ziegler},
 116   booktitle =    {Polytopes --- Combinatorics and Computation},
 117   publisher =    {Birkh\"auser},
 118   year =         {2000}
 119 }
 120
 121 @article{Stanley93monotonicity,
 122   author    = {Richard P. Stanley},
 123   title     = {A Monotonicity Property of h-vectors and h*-vectors.},
 124   journal   = {European Journal of Combinatorics},
 125   volume    = {14},
 126   number    = {3},
 127   year      = {1993},
 128   pages     = {251-258},
 129 }
 130
 131 @TechReport{ Omega_calc,
 132     author = "Wayne Kelly and Vadim Maslov and William Pugh and Evan Rosser and Tatiana Shpeisman and Dave Wonnacott",
 133     title = "The {Omega} Calculator and Library",
 134     month = nov,
 135     institution = "University of Maryland",
 136     year = 1996
 137 }
 138
 139 @TechReport{ Omega_lib,
 140     author = "Wayne Kelly and Vadim Maslov and William Pugh and Evan Rosser and Tatiana Shpeisman and Dave Wonnacott",
 141     title = "The {Omega} Library",
 142     month = nov,
 143     institution = "University of Maryland",
 144     year = 1996
 145 }
 146
 147 @inproceedings{Turjan2002,
 148     author = "Alexandru Turjan and Bart Kienhuis and Ed Deprettere",
 149     title = "A compile time based approach for solving out-of-order communication in {Kahn} Process Networks",
 150     booktitle = "IEEE 13th International Conference on Aplication-specific Systems, Architectures and Processors (ASAP'2002)",
 151     location = "San Jose, CA, USA",
 152     month = Jul,
 153     year =  2002
 154 }
 155
 156 @article{Loechner2002,
 157  author = {Vincent Loechner and Beno\^it Meister and Philippe Clauss},
 158  title = {Precise Data Locality Optimization of Nested Loops},
 159  journal = {J. Supercomput.},
 160  volume = {21},
 161  number = {1},
 162  year = {2002},
 163  issn = {0920-8542},
 164  pages = {37--76},
 165  doi = {http://dx.doi.org/10.1023/A:1013535431127},
 166  publisher = {Kluwer Academic Publishers},
 167  }
 168
 169 @inproceedings{Verdoolaege2004embedded,
 170   AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Seghir, Rachid and Loechner, Vincent",
 171   TITLE = {{A}nalytical computation of {E}hrhart polynomials and its applications for embedded systems},
 172   YEAR = {2004},
 173   booktitle = {2nd Workshop on Optimization for DSP and Embedded Systems, ODES-2},
 174   location = {Palo Alto, USA},
 175   month =  mar,
 176 }
 177
 178 @TECHREPORT{Verdoolaege2004TR,
 179   AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Seghir, Rachid and Loechner, Vincent",
 180   TITLE = {{A}nalytical computation of {E}hrhart polynomials and its applications for embedded systems},
 181   INSTITUTION = {Department of Computer Science, K.U.Leuven},
 182   YEAR = {2004},
 183   TYPE = {Report CW},
 184   NUMBER = {376},
 185   ADDRESS = {Leuven, Belgium},
 186   MONTH = {jan},
 187 NOTE = {URL = http://www.cs.kuleuven.ac.be/publicaties/rapporten/cw/CW376.abs.html},
 188 }
 189
 190 @TechReport{Seghir2004analytical,
 191         title = {Analytical Computation of {Ehrhart} Polynomials and its Application in Compile-Time Generated Cache Hints},
 192         author= {Rachid Seghir and Sven Verdoolaege and Kristof Beyls and Vincent Loechner},
 193         month = feb,
 194         year  = {2004},
 195         number = 118,
 196         institution = ICPS,
 197 }
 198
 199 @INPROCEEDINGS{Verdoolaege2004analytical,
 200   AUTHOR = "Verdoolaege, Sven and Seghir, Rachid and Beyls, Kristof and Loechner, Vincent and Bruynooghe, Maurice",
 201   TITLE = {{A}nalytical computation of {E}hrhart polynomials: {Enabling} more compiler analyses and optimizations},
 202   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}.},
 203   YEAR = {2004},
 204   pages = {248--258},
 205   month = sep,
 206 }
 207
 208 @TECHREPORT{Verdoolaege2004experiences,
 209   AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Catthoor, Francky",
 210   TITLE = {{E}xperiences with enumeration of integer projections of parametric polytopes},
 211   INSTITUTION = {K.U.Leuven, Department of Computer Science},
 212   YEAR = {2004},
 213   TYPE = {Report CW},
 214   NUMBER = {395},
 215   MONTH = oct,
 216 NOTE = {URL = http://www.cs.kuleuven.ac.be/publicaties/rapporten/cw/CW395.abs.html},
 217 }
 218
 219 @INPROCEEDINGS{Verdoolaege2005experiences,
 220   AUTHOR = "Verdoolaege, Sven and Beyls, Kristof and Bruynooghe, Maurice and Catthoor, Francky",
 221   TITLE = {{E}xperiences with enumeration of integer projections of parametric polytopes},
 222   BOOKTITLE = {{P}roceedings of 14th {I}nternational {C}onference on {C}ompiler {C}onstruction, {E}dinburgh, {S}cotland},
 223   YEAR = {2005},
 224   EDITOR = {Bodik, R.},
 225   VOLUME = 3443,
 226     pages = "91-105",
 227     series = "Lecture Notes in Computer Science",
 228     publisher = "Springer-Verlag",
 229     address = "Berlin",
 230 }
 231
 232 @TECHREPORT{Verdoolaege2005barvinok,
 233   AUTHOR = "Verdoolaege, Sven and Woods, Kevin M. and Bruynooghe, Maurice and
 234 Cools, Ronald",
 235   YEAR = {2005},
 236   TITLE = {Computation and Manipulation of Enumerators of Integer Projections of
 237  Parametric Polytopes},
 238   TYPE = {Report CW},
 239   NUMBER = {392},
 240   INSTITUTION = {Dept.\ of Computer Science, K.U.Leuven},
 241   ADDRESS = {Leuven, Belgium},
 242 }
 243
 244 @misc{Verdoolaege2007counting,
 245     title = {{Counting with rational generating functions}},
 246     author = {Sven Verdoolaege and Kevin M. Woods},
 247     year = 2007,
 248     eprint = {arXiv:math.CO/0504059},
 249     note = "To appear in The Journal of Symbolic Computation",
 250 }
 251
 252 @article{Verdoolaege2007parametric,
 253     author = "S. Verdoolaege and R. Seghir and K. Beyls and V. Loechner and M. Bruynooghe",
 254     title = "Counting integer points in parametric polytopes using {Barvinok}'s rational functions",
 255     journal = "Algorithmica",
 256     year = 2007,
 257     volume = 48,
 258     number = 1,
 259     month = jun,
 260     publisher = "Springer New York",
 261     pages = "37--66",
 262 }
 263
 264 @INPROCEEDINGS{Seghir2006memory,
 265   AUTHOR = "Rachid Seghir and Vincent Loechner",
 266   TITLE = {Memory Optimization by Counting Points in Integer Transformations of Parametric Polytopes},
 267   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},
 268   month = oct,
 269   YEAR = {2006}
 270 }
 271
 272 @article{Koeppe2006primal,
 273     title = {{A primal Barvinok algorithm based on irrational decompositions}},
 274     author = {Matthias K\"oppe},
 275   year =         2007,
 276   journal =      {SIAM Journal on Discrete Mathematics},
 277   volume = 21,
 278   number = 1,
 279   pages = {220--236},
 280   doi = {10.1137/060664768},
 281 }
 282
 283 @MISC{Beck2005Brion,
 284   author = {Matthias Beck and Christian Haase and Frank Sottile},
 285   title = {Theorems of {Brion}, {Lawrence}, and {Varchenko} on rational generating  functions for cones},
 286   url = {http://www.citebase.org/abstract?id=oai:arXiv.org:math/0506466},
 287   year = {2005}
 288 }
 289
 290 @article{Lasserre2005alternative,
 291     author = "Jean B. Lasserre and Eduardo S. Zeron",
 292     title = "An alternative algorithm for counting lattice points in a convex polytope",
 293     year = 2005,
 294     volume = 30,
 295     page = "597--614",
 296     journal = "Math. Oper. Res.",
 297 }
 298
 299 @article{Beyls2005hints,
 300 author= {Beyls, Kristof and  D'Hollander, Erik},
 301 title= {Generating Cache Hints for Improved Program Efficiency},
 302 journal= {Journal of Systems Architecture},
 303 year= {2005},
 304 month= {4},
 305 volume= {51},
 306 number= {4},
 307 pages= {223-250},
 308 publisher= {Elsevier},
 309 }
 310
 311 @TechReport{CFGV06,
 312   author       = {Clauss, P. and Fern\'andez, F. J. and Gabervetsky, D. and Verdoolaege, S.},
 313   title        = {Symbolic Polynomial Maximization over Convex Sets and its Application to Memory Requirement Estimation},
 314   institution  = {Universit\'e Louis Pasteur},
 315   number       = {06-04},
 316   month        = oct,
 317   year         = {2006},
 318   type         = {ICPS Research Report},
 319   url          = {http://icps.u-strasbg.fr/upload/icps-2006-173.pdf},
 320 }
 321
 322 @article{Cook1993implementation,
 323 AUTHOR={William Cook and Thomas Rutherford and Herbert E. Scarf and David F. Shallcross},
 324 TITLE={An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming},
 325 YEAR=1993,
 326 journal = "ORSA Journal on Computing",
 327 volume = 5,
 328 number = 2,
 329 }
 330
 331 @misc{GLPK,
 332 author = "Andrew Makhorin",
 333 title = "GNU Linear Programming Kit, Reference Manual, Version 4.11",
 334 year = 2006,
 335 month = jul,
 336 }
 337
 338 @inproceedings{Verdoolaege2006odes,
 339   AUTHOR = "Verdoolaege, Sven and Nikolov, Hristo and Stefanov, Todor",
 340   TITLE = {Improved Derivation of Process Networks},
 341   YEAR = {2006},
 342   booktitle = {4th Workshop on Optimization for DSP and Embedded Systems, ODES-4},
 343   location = {New York, USA},
 344   month =  mar,
 345 }
 346
 347 @article{Verdoolaege2007pn,
 348   AUTHOR = "Verdoolaege, Sven and Nikolov, Hristo and Stefanov, Todor",
 349   TITLE = {pn: A Tool for Improved Derivation of Process Networks},
 350   YEAR = {2007},
 351   volume = 2007,
 352   journal = "EURASIP Journal on Embedded Systems, special issue on
 353             Embedded Digital Signal Processing Systems",
 354   doi = {10.1155/2007/75947},
 355   publisher = "Hindawi Publishing Corporation",
 356 }
 357
 358 @article{Scarf2006Neighborhood,
 359   author    = {Herbert E. Scarf and
 360                Kevin M. Woods},
 361   title     = {Neighborhood Complexes and Generating Functions for Affine
 362                Semigroups.},
 363   journal   = {Discrete {\&} Computational Geometry},
 364   volume    = {35},
 365   number    = {3},
 366   year      = {2006},
 367   pages     = {385-403},
 368   ee        = {http://dx.doi.org/10.1007/s00454-005-1222-y},
 369   bibsource = {DBLP, http://dblp.uni-trier.de}
 370 }
 371
 372 @ARTICLE{Scarf1981indivisibilities:II,
 373 AUTHOR={Scarf, Herbert E},
 374 TITLE={Production Sets with Indivisibilities-Part {II}: The Case of Two Activities},
 375 JOURNAL={Econometrica},
 376 YEAR=1981,
 377 VOLUME={49},
 378 NUMBER={2},
 379 PAGES={395-423},
 380 MONTH=Mar,
 381 }
 382
 383 @phdthesis{Meister2004PhD,
 384     title = {Stating and Manipulating Periodicity in the Polytope Model. Applications to Program Analysis and Optimization},
 385     author= {Beno\^it Meister},
 386     institution = {Universit\'e Louis Pasteur},
 387     month = Dec,
 388     year  = {2004},
 389     school = ICPS,
 390 }
 391
 392 @article{Feautrier88parametric,
 393     author = "P. Feautrier",
 394     title = "Parametric Integer Programming",
 395     journal = "Operationnelle/Operations Research",
 396     volume = "22",
 397     number = "3",
 398     pages = "243--268",
 399     year = "1988",
 400     url = "citeseer.nj.nec.com/feautrier88parametric.html",
 401 }
 402
 403 @InProceedings{Gomory1963,
 404   author       = "R. E. Gomory",
 405   editor       = "R. L. Graves and P. Wolfe",
 406   booktitle    = "Recent Advances in Mathematical Programming",
 407   title        = "An algorithm for integer solutions to linear programming",
 408   publisher    = "McGraw-Hill",
 409   address      = "New York",
 410   pages        = "269--302",
 411   year         = "1963",
 412 }
 413
 414 @misc{Feautrier:PIP,
 415     author = "Paul Feautrier",
 416     title = "Solving Systems of Affine (In)Equalities: {PIP}'s User's Guide",
 417     year = 2006,
 418 }
 419
 420 @inproceedings{Barvinok1992volume,
 421  author = {Alexander I. Barvinok},
 422  title = {Computing the volume, counting integral points, and exponential sums},
 423  booktitle = {Proceedings of the eighth annual symposium on Computational geometry},
 424  year = {1992},
 425  isbn = {0-89791-517-8},
 426  pages = {161--170},
 427  location = {Berlin, Germany},
 428  doi = {http://doi.acm.org/10.1145/142675.142713},
 429  publisher = {ACM Press},
 430 }
 431
 432 @misc{Koeppe2006experiments,
 433     title = "Experiments with an algebraic scheme for estimating the number of lattice points in polyhedra",
 434     author = {De Loera, Jes\'us A. and Matthias K\"oppe},
 435     year = 2006,
 436     note = "Manuscript in preparation",
 437 }
 438
 439 @article{DeLoera2003effective,
 440     title = "Effective Lattice Point Counting in Rational Convex Polytopes",
 441     author = "De Loera, Jes\'us A. and Raymond Hemmecke and
 442               Jeremiah Tauzer and Ruriko Yoshida",
 443     year = 2004,
 444     journal = "The Journal of Symbolic Computation",
 445     volume = 38,
 446     number = 4,
 447     pages = "1273--1302",
 448     url = "http://www.math.ucdavis.edu/~latte/theory.html",
 449 }
 450
 451 @article{Barvinok1994,
 452     author = "A. I. Barvinok",
 453     title = "Computing the {Ehrhart} polynomial of a convex lattice polytope",
 454     journal = "Dicrete Comput. Geom.",
 455     volume =  12,
 456     year = 1994,
 457     pages = "35--48",
 458 }
 459
 460 @article {Brion88,
 461     AUTHOR = {Brion, Michel},
 462      TITLE = {Points entiers dans les poly\`edres convexes},
 463    JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
 464   FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
 465               Quatri\`eme S\'erie},
 466     VOLUME = {21},
 467       YEAR = {1988},
 468     NUMBER = {4},
 469      PAGES = {653--663},
 470       ISSN = {0012-9593},
 471      CODEN = {ASENAH},
 472    MRCLASS = {52A43 (11H06 12L10 14F12 32C40)},
 473   MRNUMBER = {90d:52020},
 474 MRREVIEWER = {Daniel Barlet},
 475 }
 476
 477 @misc{Koeppe2007parametric,
 478     title = {Computing parametric rational generating functions
 479   with a primal Barvinok algorithm},
 480     author = {Matthias K\"oppe and Sven Verdoolaege},
 481     year = 2007,
 482     note = "manuscript in preparation",
 483 }
 484
 485 @article{Lepelley2007,
 486     author =       {Dominique Lepelley and Ahmed Louichi and Hatem Smaoui},
 487     title =        {On {Ehrhart} Polynomials and Probability
 488                     Calculations in Voting Theory},
 489     journal =      "Social Choice and Welfare",
 490     year =         {2007},
 491     month =        Apr,
 492     Publisher =    "Springer Berlin / Heidelberg",
 493     ISSN =         "0176-1714 (Print) 1432-217X (Online)",
 494     DOI =           "10.1007/s00355-007-0236-1",
 495 }
 496
 497 @article{Barvinok2006simplex,
 498   author =       {Barvinok, Alexander I.},
 499   title =        {Computing the {Ehrhart} quasi-polynomial of a rational simplex},
 500   year =         2006,
 501   pages =        "1449-1466",
 502   volume =       75,
 503   journal =      "Math. Comp.",
 504   PUBLISHER = {American Mathematical Society},
 505 }
 506
 507 @mastersthesis{Rabl2006,
 508     title = "Volume Calculation and Estimation of Parameterized Integer Polytopes",
 509     author = "Tilmann Rabl",
 510     month = jan,
 511     school = Passau,
 512     year = 2006,
 513 }
 514
 515 @book{ Ehrhart1977,
 516     author = "E. Ehrhart",
 517     title = "Polyn\^omes arithm\'etiques et M\'ethode des Poly\`edres en Combinatoire",
 518     series = "International Series of Numerical Mathematics",
 519     volume = 35,
 520     publisher = "Birkhauser Verlag",
 521     address =  "Basel/Stuttgart",
 522     year = 1977,
 523 }
 524
 525 @book{Stanley1986,
 526     author =       "Richard P. Stanley",
 527     title =        "Enumerative Combinatorics",
 528     volume =     1,
 529     publisher =    "Cambridge University Press",
 530     year = 1986,
 531 }
 532
 533 @misc{Woods2006personal,
 534     author = "Kevin M. Woods",
 535     title = "personal communication",
 536     year = 2006,
 537     month = jun,
 538 }
 539
 540 @Techreport{Pop06,
 541   Author = "S. Pop and G.-A. Silber and A. Cohen and C. Bastoul
 542             and S. Girbal and N. Vasilache",
 543   Title = "{GRAPHITE}: Polyhedral Analyses and Optimizations for {GCC}",
 544   Number = "A/378/CRI",
 545   Institution = "Centre de Recherche en Informatique,
 546                  \'Ecole des Mines de Paris",
 547   Address = "Fontainebleau, France",
 548   Year = 2006,
 549   Note = "Contribution to the GNU Compilers Collection Developers Summit 2006
 550           (GCC Summit 06), Ottawa, Canada, June 28--30, 2006",
 551   Abstract = "We present a plan to add loop nest optimizations in GCC
 552               based on polyhedral representations of loop nests. We
 553               advocate a static analysis approach based on a hierarchy
 554               of interchangeable abstractions with solvers that range
 555               from the exact solvers such as OMEGA, to faster but less
 556               precise solvers based on more coarse abstractions. The
 557               intermediate representation GRAPHITE (GIMPLE Represented
 558               as Polyhedra with Interchangeable Envelopes), built on
 559               GIMPLE and the natural loops, hosts the high level loop
 560               transformations. We base this presentation on the
 561               WRaP-IT project developed in the Alchemy group at INRIA
 562               Futurs and Paris-Sud University, on the PIPS compiler
 563               developed at \'Ecole des mines de Paris, and on a joint
 564               work with several members of the static analysis and
 565               polyhedral compilation community in France.
 566
 567               The main goal of this project is to bring more high
 568               level loop optimizations to GCC: loop fusion, tiling,
 569               strip mining, etc. Thanks to the WRaP-IT experience, we
 570               know that the polyhedral analyzes and transformations
 571               are affordable in a production compiler. A second goal
 572               of this project is to experiment with compile time
 573               reduction versus attainable precision when replacing
 574               operations on polyhedra with faster operations on more
 575               abstract domains. However, the use of a too coarse
 576               representation for computing might also result in an
 577               over approximated solution that cannot be used in
 578               subsequent computations. There exists a trade off
 579               between speed of the computation and the attainable
 580               precision that has not yet been analyzed for real world
 581               programs."
 582 }
 583
 584 @article{Baldoni2006,
 585   author    = {Baldoni-Silva, M. Welleda and
 586                Matthias Beck and
 587                Charles Cochet and
 588                Mich{\`e}le Vergne},
 589   title     = {Volume Computation for Polytopes and Partition Functions
 590                for Classical Root Systems.},
 591   journal   = {Discrete {\&} Computational Geometry},
 592   volume    = {35},
 593   number    = {4},
 594   year      = {2006},
 595   pages     = {551-595},
 596   ee        = {http://dx.doi.org/10.1007/s00454-006-1234-2},
 597   bibsource = {DBLP, http://dblp.uni-trier.de}
 598 }
 599
 600 @MISC{Meister2007b,
 601   author = {Beno\^it Meister and Sven Verdoolaege},
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 603          by Polynomials},
 604   year = {2007},
 605   note = {manuscript in preparation},
 606 }
 607
 608 @misc{Devos2007,
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 610     author = {Harald Devos and Sven Verdoolaege and Van Campenhout, Jan and
 611               Dirk Stroobandt},
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 613     note = "manuscript in preparation",
 614 }
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 638 }
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 643     journal =  "Applied Geometry and Discrete Mathematics --- The Victor Klee Festschrift",
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 654     school = "Cornell University",
 655     month =  May,
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 660     series = "Pure and applied mathematics",
 661     AUTHOR = {Henrici, Peter},
 662      TITLE = {Applied and Computational Complex Analysis},
 663       NOTE = {Volume 1: Power series---integration---conformal
 664               mapping---location of zeros,
 665               Pure and Applied Mathematics},
 666  PUBLISHER = {Wiley-Interscience [John Wiley \& Sons]},
 667    ADDRESS = {New York},
 668       YEAR = {1974},
 669      PAGES = {xv+682},
 670    MRCLASS = {30-02 (65E05)},
 671   MRNUMBER = {MR0372162 (51 \#8378)},
 672 MRREVIEWER = {M. Marden},
 673 }
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 675 @article{Barvinok1999,
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 677     title = "An algorithmic theory of lattice points in polyhedra",
 678     journal = "New Perspectives in Algebraic Combinatorics",
 679     series = "MSRI book series",
 680     volume =  "38",
 681     pages = "91--147",
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 683     year = 1999,
 684 }
 685
 686 @Misc{latte-macchiato,
 687   author =       {K\"oppe, Matthias},
 688   title =        {{LattE macchiato}, version 1.2-mk-0.7.1, an improved version of {De Loera}
 689                   et al.'s {LattE} program for counting integer points in
 690                   polyhedra with variants of {Barvinok}'s algorithm},
 691   howpublished = {Available from URL {\url{http://www.math.uni-magdeburg.de/~mkoeppe/latte/}}}
 692 ,
 693   year = 2006
 694 }
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 696 @inproceedings{Tawbi1994,
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 698     title = "Estimation of Nested Loops execution time by Integer Arithmetic in Convex Polyhedra",
 699     booktitle = "Proceedings of the 8th International Parallel Processing Symposium",
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 701     pages =  "217--221",
 702     year = 1994,
 703 }
 704
 705 @inproceedings{Sakellariou1997sums,
 706     author = "Rizos Sakellariou",
 707     title = "Symbolic Evaluation of Sums for Parallelising Compilers",
 708     editor = "A. Sydow",
 709     booktitle = "Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics",
 710     location = "Berlin",
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 718 @article{VanEngelen2004,
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 720  title =        {Parametric Timing Estimation With the {N}ewton-{G}regory Formulae},
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 722  volume =       {18},
 723  number =       {10},
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 727  pages =        {1434--1464},
 728  publisher =    {Wiley Press, USA},
 729 }
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 731 @misc{Berline2006local,
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 733     author = "Nicole Berline and Mich\`ele Vergne",
 734     year = 2006,
 735     month = jul,
 736     note = "http://arXiv.org/abs/math/0507256",
 737 }
 738
 739 @misc{Berline2007personal,
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 744 }
 745
 746 @inproceedings{Eisenschmidt2007integrally,
 747         author = {Eisenschmidt, Elke and K\"oppe, Matthias},
 748         title = "Integrally  indecomposable polytopes and the survivable network design problem",
 749         note = "To appear",
 750         booktitle = "Electronic proceedings of the 6th International Workshop on the Design of Reliable Communication Networks, DRCN 2007",
 751         locationg = "La Rochelle, France",
 752         year = 2007,
 753 }
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 755 @inproceedings{Pfeifle2003,
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 757                J{\"o}rg Rambau},
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 759   booktitle = {Algebra, Geometry, and Software Systems},
 760   year      = {2003},
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 763   editor    = {Michael Joswig and
 764                Nobuki Takayama},
 765 }
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 774 @PhdThesis{Eisenbrand2000PhD,
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 777     school = {Universit\"at des Saarlandes},
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 791 }
 792
 793 @Misc{4ti2,
 794   author =   {
 795   Ralf Hemmecke and
 796   Raymond Hemmecke and
 797   Matthias K\"oppe and
 798   Peter Malkin and
 799   Matthias Walter},
 800   title =    {4ti2 -- A software package for algebraic, geometric and
 801               combinatorial problems on linear spaces},
 802   howpublished = {Available at \url{www.4ti2.de}}
 803 }
 804
 805 @inproceedings{Hemmecke2002Hilbert,
 806     author = "R. Hemmecke",
 807     title = "On the Computation of Hilbert Bases of Cones",
 808     bookttile = "Mathematical Software, ICMS 2002",
 809     editor = "A. M. Cohen and X.-S. Gao and N. Takayama",
 810     publisher = "World Scientific",
 811     year = 2002,
 812 }
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 814 @misc{Eisenbrand2007parameterised,
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 816     title = "Integer points in a parameterised polyhedron",
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 820 @article{Kannan1992,
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 829
 830 @phdthesis{Woods2004PhD,
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 832     title = "Rational Generating Functions and Lattice Point Sets",
 833     school = "University of Michigan",
 834     year =  2004,
 835 }
 836
 837 @misc{Koeppe2007personal,
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 839     title = "personal communication",
 840     year = 2007,
 841     month = jun,
 842 }
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 844 @book {Barvinok02,
 845     AUTHOR = {Barvinok, Alexander},
 846      TITLE = {A {C}ourse in {C}onvexity},
 847     SERIES = {Graduate Studies in Mathematics},
 848     VOLUME = {54},
 849  PUBLISHER = {American Mathematical Society},
 850    ADDRESS = {Providence, RI},
 851       YEAR = {2002},
 852      PAGES = {x+366},
 853       ISBN = {0-8218-2968-8},
 854    MRCLASS = {52-02 (49N15 52-01 90-02 90C05 90C22 90C25)},
 855   MRNUMBER = {2003j:52001},
 856 MRREVIEWER = {P. McMullen},
 857 }
 858
 859 @article{Lagarias90,
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 861                Lenstra, Jr., Hendrik W. and
 862                Claus-Peter Schnorr},
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 864                and its reciprocal lattice},
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 867   number    = {4},
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 875                L{\'a}szl{\'o} Lov{\'a}sz and
 876                William R. Pulleyblank},
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 880   number    = {3},
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 884 }
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 886 @article{Cook1992,
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 888     year = 1992,
 889     title = "On integer points in polyhedra",
 890     journal = "Combinatorica",
 891     volume =  12,
 892     number = 1,
 893     pages = "27--37",
 894 }
 895
 896 @phdthesis{Hartmann1989PhD,
 897  author = {Mark Evan Hartmann},
 898  title = {Cutting planes and the complexity of the integer hull},
 899  year = {1989},
 900  order_no = {AAI8915096},
 901  publisher = {Cornell University},
 902  address = {Ithaca, NY, USA},
 903  }
 904
 905 @inproceedings{Huggins06,
 906   author    = {Peter Huggins},
 907   title     = {{\it iB4e}: A Software Framework for Parametrizing Specialized
 908                {LP} Problems},
 909   booktitle = {ICMS 2006, Proceedings of the Second International
 910                Congress on Mathematical Software},
 911   editor    = {Andr{\'e}s Iglesias and
 912                Nobuki Takayama},
 913   year      = {2006},
 914   pages     = {245-247},
 915   ee        = {http://dx.doi.org/10.1007/11832225_24},
 916   publisher = {Springer},
 917   series    = {Lecture Notes in Computer Science},
 918   volume    = {4151},
 919   bibsource = {DBLP, http://dblp.uni-trier.de},
 920 }
 921
 922 @book{Preparata1985,
 923         abstract = {{From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical  Journal#2}},
 924         author = {Preparata, Franco  P.  and Shamos, Michael  I. },
 925         citeulike-article-id = {935971},
 926         howpublished = {Hardcover},
 927         isbn = {0387961313},
 928         keywords = {algorithm, computational, computing, geometry},
 929         month = {August},
 930         priority = {0},
 931         publisher = {Springer},
 932         title = {Computational Geometry: An Introduction (Monographs in Computer Science)},
 933         year = {1985}
 934 }
 935
 936 @article{Woods2005period,
 937         title = "Computing the period of an {Ehrhart} quasi-polynomial",
 938         author = "Kevin M. Woods",
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 940         volume = 12,
 941         year = 2005,
 942         pages = "R34",
 943 }
 944
 945 @article{Woods2003short,
 946     year = 2003,
 947     Journal = "J. Amer. Math. Soc.",
 948     volume =  16,
 949     pages = "957--979",
 950     month = apr,
 951     title = {{Short rational generating functions for lattice point
 952         problems}},
 953     author = {Alexander I. Barvinok and Kevin Woods},
 954 }
 955
 956 @article{Banaszczyk1999flatness,
 957     title = "The Flatness Theorem for nonsymmetric convex bodies via the local theory of Banach spaces",
 958     author = "Banaszczyk, Wojciech and Litvak, Alexander E. and Pajor, A. and Szarek, S. J.",
 959     journal = "Mathematics of Operations Research",
 960     month =  Aug,
 961     year = 1999,
 962     volume =  24,
 963     number =  3,
 964     pages = "728--750",
 965 }