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literature.bib
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@article {MR0438810,
AUTHOR = {Stockmeyer, Larry J.},
TITLE = {The polynomial-time hierarchy},
JOURNAL = {Theoret. Comput. Sci.},
FJOURNAL = {Theoretical Computer Science},
VOLUME = {3},
YEAR = {1976},
NUMBER = {1},
PAGES = {1--22 (1977)},
ISSN = {0304-3975},
MRCLASS = {68A20},
MRNUMBER = {0438810 (55 \#11716)},
MRREVIEWER = {John T. Gill},
}
@article {MR1304623,
AUTHOR = {Barvinok, Alexander},
TITLE = {A polynomial time algorithm for counting integral points in
polyhedra when the dimension is fixed},
JOURNAL = {Math. Oper. Res.},
FJOURNAL = {Mathematics of Operations Research},
VOLUME = {19},
YEAR = {1994},
NUMBER = {4},
PAGES = {769--779},
ISSN = {0364-765X},
MRCLASS = {52C07 (52B55 90C10)},
MRNUMBER = {1304623 (96c:52026)},
MRREVIEWER = {Colin J. H. McDiarmid},
DOI = {10.1287/moor.19.4.769},
URL = {http://dx.doi.org/10.1287/moor.19.4.769},
}
@article {MR0438811,
AUTHOR = {Wrathall, Celia},
TITLE = {Complete sets and the polynomial-time hierarchy},
JOURNAL = {Theoret. Comput. Sci.},
FJOURNAL = {Theoretical Computer Science},
VOLUME = {3},
YEAR = {1976},
NUMBER = {1},
PAGES = {23--33 (1977)},
ISSN = {0304-3975},
MRCLASS = {68A20},
MRNUMBER = {0438811 (55 \#11717)},
MRREVIEWER = {John T. Gill},
}
@article {MR1234309,
AUTHOR = {Morelli, Robert},
TITLE = {Pick's theorem and the {T}odd class of a toric variety},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {100},
YEAR = {1993},
NUMBER = {2},
PAGES = {183--231},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {14M25 (14C40 52B20)},
MRNUMBER = {1234309 (94j:14048)},
MRREVIEWER = {G. K. Sankaran},
DOI = {10.1006/aima.1993.1033},
URL = {http://dx.doi.org/10.1006/aima.1993.1033},
}
@article {MR2464645,
AUTHOR = {Eisenbrand, Friedrich and Shmonin, Gennady},
TITLE = {Parametric integer programming in fixed dimension},
JOURNAL = {Math. Oper. Res.},
FJOURNAL = {Mathematics of Operations Research},
VOLUME = {33},
YEAR = {2008},
NUMBER = {4},
PAGES = {839--850},
ISSN = {0364-765X},
MRCLASS = {90C10 (90C60)},
MRNUMBER = {2464645 (2009j:90078)},
MRREVIEWER = {K. G. Murty},
DOI = {10.1287/moor.1080.0320},
URL = {http://dx.doi.org/10.1287/moor.1080.0320},
}
@article {MR1179254,
AUTHOR = {Kannan, Ravi},
TITLE = {Lattice translates of a polytope and the {F}robenius problem},
JOURNAL = {Combinatorica},
FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
the Theory of Computing},
VOLUME = {12},
YEAR = {1992},
NUMBER = {2},
PAGES = {161--177},
ISSN = {0209-9683},
CODEN = {COMBDI},
MRCLASS = {52B55 (52C07 90C60)},
MRNUMBER = {1179254 (93k:52015)},
MRREVIEWER = {Gerard Sierksma},
DOI = {10.1007/BF01204720},
URL = {http://dx.doi.org/10.1007/BF01204720},
}
@article {MR839604,
AUTHOR = {Cook, William and Gerards, Albert M. H. and Schrijver, Alexander and Tardos,
{\'E}va},
TITLE = {Sensitivity theorems in integer linear programming},
JOURNAL = {Math. Programming},
FJOURNAL = {Mathematical Programming},
VOLUME = {34},
YEAR = {1986},
NUMBER = {3},
PAGES = {251--264},
ISSN = {0025-5610},
CODEN = {MHPGA4},
MRCLASS = {90C10},
MRNUMBER = {839604 (87i:90159)},
MRREVIEWER = {C. B. Millham},
DOI = {10.1007/BF01582230},
URL = {http://dx.doi.org/10.1007/BF01582230},
}
@incollection {MR1105115,
AUTHOR = {Kannan, Ravi},
TITLE = {Test sets for integer programs, {$\forall\exists$} sentences},
BOOKTITLE = {Polyhedral combinatorics ({M}orristown, {NJ}, 1989)},
SERIES = {DIMACS Ser. Discrete Math. Theoret. Comput. Sci.},
VOLUME = {1},
PAGES = {39--47},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1990},
MRCLASS = {90C10 (03D15)},
MRNUMBER = {1105115 (92c:90079)},
MRREVIEWER = {Joachim Piehler},
}
@incollection {MR2011752,
AUTHOR = {Kaibel, Volker and Pfetsch, Marc E.},
TITLE = {Some algorithmic problems in polytope theory},
BOOKTITLE = {Algebra, geometry, and software systems},
PAGES = {23--47},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2003},
MRCLASS = {52B55 (68Q25 90C57)},
MRNUMBER = {2011752 (2004i:52012)},
}
@article {MR1450863,
AUTHOR = {Sch{\"o}ning, U.},
TITLE = {Complexity of {P}resburger arithmetic with fixed quantifier
dimension},
JOURNAL = {Theory Comput. Syst.},
FJOURNAL = {Theory of Computing Systems},
VOLUME = {30},
YEAR = {1997},
NUMBER = {4},
PAGES = {423--428},
ISSN = {1432-4350},
CODEN = {TCSYFI},
MRCLASS = {03D15 (03F30 68Q15 68Q25)},
MRNUMBER = {1450863 (98k:03092)},
DOI = {10.1007/s002240000059},
URL = {http://dx.doi.org/10.1007/s002240000059},
}
@article {MR946203,
AUTHOR = {Gr{\"a}del, Erich},
TITLE = {Subclasses of {P}resburger arithmetic and the polynomial-time
hierarchy},
JOURNAL = {Theoret. Comput. Sci.},
FJOURNAL = {Theoretical Computer Science},
VOLUME = {56},
YEAR = {1988},
NUMBER = {3},
PAGES = {289--301},
ISSN = {0304-3975},
CODEN = {TCSDI},
MRCLASS = {03D15 (03F30 68Q15)},
MRNUMBER = {946203 (89m:03030)},
MRREVIEWER = {Peter Slessenger},
DOI = {10.1016/0304-3975(88)90136-3},
URL = {http://dx.doi.org/10.1016/0304-3975(88)90136-3},
}
@article {Santos10,
author = {Francisco Santos},
title = {A counterexample to the {H}irsch conjecture},
ABBRJOURNAL = {Ann. of Math.},
JOURNAL = {Annals of Mathematics},
VOLUME = {176},
YEAR = {2012},
NUMBER = {1},
PAGES = {383--412},
DOI = {10.4007/annals.2012.176.1.7},
}
@article {MR1486304,
AUTHOR = {Orlin, James B.},
TITLE = {A polynomial time primal network simplex algorithm for minimum
cost flows},
NOTE = {Network optimization: algorithms and applications (San
Miniato, 1993)},
JOURNAL = {Mathematical Programming},
VOLUME = {78},
YEAR = {1997},
NUMBER = {2, Ser. B},
PAGES = {109--129},
ISSN = {0025-5610},
CODEN = {MHPGA4},
MRCLASS = {90C35 (68Q25)},
MRNUMBER = {1486304 (99c:90149)},
MRREVIEWER = {Prabir Das},
DOI = {10.1016/S0025-5610(97)00011-7},
URL = {http://dx.doi.org/10.1016/S0025-5610(97)00011-7},
}
@article {MR2223631,
AUTHOR = {Brightwell, Graham and van den Heuvel, Jan and Stougie, Leen},
TITLE = {A linear bound on the diameter of the transportation polytope},
JOURNAL = {Combinatorica},
FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
the Theory of Computing},
VOLUME = {26},
YEAR = {2006},
NUMBER = {2},
PAGES = {133--139},
ISSN = {0209-9683},
MRCLASS = {90C27 (90C08)},
MRNUMBER = {2223631 (2008c:90052)},
MRREVIEWER = {Sheng Bau},
DOI = {10.1007/s00493-006-0010-5},
URL = {http://dx.doi.org/10.1007/s00493-006-0010-5},
}
@article {MR769400,
AUTHOR = {Balinski, Michel Louis},
TITLE = {The {H}irsch conjecture for dual transportation polyhedra},
JOURNAL = {Math. Oper. Res.},
FJOURNAL = {Mathematics of Operations Research},
VOLUME = {9},
YEAR = {1984},
NUMBER = {4},
PAGES = {629--633},
ISSN = {0364-765X},
MRCLASS = {90B10 (05C35 52A25)},
MRNUMBER = {769400 (86c:90038)},
MRREVIEWER = {E. Gabowitsch},
DOI = {10.1287/moor.9.4.629},
URL = {http://dx.doi.org/10.1287/moor.9.4.629},
}
@article {MR2568801,
AUTHOR = {De Loera, Jes{\'u}s A. and Kim, Edward D. and Onn, Shmuel and
Santos, Francisco},
TITLE = {Graphs of transportation polytopes},
JOURNAL = {J. Combin. Theory Ser. A},
FJOURNAL = {Journal of Combinatorial Theory. Series A},
VOLUME = {116},
YEAR = {2009},
NUMBER = {8},
PAGES = {1306--1325},
ISSN = {0097-3165},
CODEN = {JCBTA7},
MRCLASS = {05C12 (05C90 90B06)},
MRNUMBER = {2568801 (2010m:05094)},
DOI = {10.1016/j.jcta.2009.03.010},
URL = {http://dx.doi.org/10.1016/j.jcta.2009.03.010},
}
@article {MR2681516,
AUTHOR = {Kim, Edward D. and Santos, Francisco},
TITLE = {An update on the {H}irsch conjecture},
JOURNAL = {Jahresber. Dtsch. Math.-Ver.},
FJOURNAL = {Jahresbericht der Deutschen Mathematiker-Vereinigung},
VOLUME = {112},
YEAR = {2010},
NUMBER = {2},
PAGES = {73--98},
ISSN = {0012-0456},
MRCLASS = {52B05 (05C10 05C12 90C08)},
MRNUMBER = {2681516 (2011f:52014)},
}
@article {MR1130448,
AUTHOR = {Kalai, Gil and Kleitman, Daniel J.},
TITLE = {A quasi-polynomial bound for the diameter of graphs
of polyhedra},
JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
FJOURNAL = {American Mathematical Society. Bulletin. New Series},
VOLUME = 26,
YEAR = 1992,
NUMBER = 2,
PAGES = {315--316},
ISSN = {0273-0979},
CODEN = {BAMOAD},
MRCLASS = {52B55},
MRNUMBER = {MR1130448 (92h:52017)},
MRREVIEWER = {W. J. Firey},
}
@article {MR2529774,
AUTHOR = {Vershynin, Roman},
TITLE = {Beyond {H}irsch conjecture: walks on random polytopes and
smoothed complexity of the simplex method},
JOURNAL = {SIAM J. Comput.},
FJOURNAL = {SIAM Journal on Computing},
VOLUME = {39},
YEAR = {2009},
NUMBER = {2},
PAGES = {646--678},
ISSN = {0097-5397},
MRCLASS = {68Q25 (52A22 68W40)},
MRNUMBER = {2529774 (2011g:68123)},
DOI = {10.1137/070683386},
URL = {http://dx.doi.org/10.1137/070683386},
}
@article {MR1274170,
AUTHOR = {Dyer, Martin and Frieze, Alan},
TITLE = {Random walks, totally unimodular matrices, and a randomised
dual simplex algorithm},
SJOURNAL = {Math. Programming},
JOURNAL = {Mathematical Programming},
VOLUME = {64},
YEAR = {1994},
NUMBER = {1, Ser. A},
PAGES = {1--16},
ISSN = {0025-5610},
CODEN = {MHPGA4},
MRCLASS = {90C05 (60J15)},
MRNUMBER = {1274170 (95c:90068)},
MRREVIEWER = {Douglas John White},
DOI = {10.1007/BF01582563},
URL = {http://dx.doi.org/10.1007/BF01582563},
}
@article {MR0355826,
AUTHOR = {Barnette, David},
TITLE = {An upper bound for the diameter of a polytope},
JOURNAL = {Discrete Math.},
FJOURNAL = {Discrete Mathematics},
VOLUME = {10},
YEAR = {1974},
PAGES = {9--13},
ISSN = {0012-365X},
MRCLASS = {52A25},
MRNUMBER = {0355826 (50 \#8300)},
MRREVIEWER = {P. McMullen},
}
@article {MR0254735,
AUTHOR = {Larman, David G.},
TITLE = {Paths of polytopes},
JOURNAL = {Proc. London Math. Soc. (3)},
FJOURNAL = {Proceedings of the London Mathematical
Society. Third Series},
VOLUME = {20},
YEAR = {1970},
PAGES = {161--178},
ISSN = {0024-6115},
MRCLASS = {52.10},
MRNUMBER = {MR0254735 (40 \#7942)},
MRREVIEWER = {P. McMullen},
}
@ARTICLE{Naddef89,
AUTHOR = {Denis Naddef},
JOURNAL = {Mathematical Programming},
PAGES = {109-110},
TITLE = {The {H}irsch conjecture is true for (0,1)-polytopes},
VOLUME = {45},
YEAR = {1989}
}
@Article{EHRR10,
author = {Friedrich Eisenbrand and Nicolai H{\"a}hnle and Alexander Razborov and Thomas Rothvo\ss},
title = {Diameter of Polyhedra: {L}imits of Abstraction},
journal = {Mathematics of Operations Research},
year = 2010,
volume = 35,
number = 4,
pages = {786-794}
}
@article {MR0206823,
AUTHOR = {Klee, Victor and Walkup, David W.},
TITLE = {The {$d$}-step conjecture for polyhedra of dimension
{$d<6$}},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {117},
YEAR = {1967},
PAGES = {53--78},
ISSN = {0001-5962},
MRCLASS = {52.40 (52.10)},
MRNUMBER = {0206823 (34 \#6639)},
MRREVIEWER = {G. T. Sallee},
}
@article{lovasz1993random,
title={Random walks in a convex body and an improved volume algorithm},
author={Lov{\'a}sz, L{\'a}szl{\'o} and Simonovits, M.},
journal={Random structures \& algorithms},
volume={4},
number={4},
pages={359--412},
year={1993},
publisher={Wiley Online Library}
}
@article{merkle1996logarithmic,
title={Logarithmic convexity and inequalities for the gamma function},
author={Merkle, Milan},
journal={Journal of mathematical analysis and applications},
volume={203},
number={2},
pages={369--380},
year={1996},
publisher={New York, Academic Press.}
}
@incollection {MR1116365,
AUTHOR = {Kalai, Gil},
TITLE = {The diameter of graphs of convex polytopes and {$f$}-vector
theory},
BOOKTITLE = {Applied geometry and discrete mathematics},
SERIES = {DIMACS Ser. Discrete Math. Theoret. Comput. Sci.},
VOLUME = {4},
PAGES = {387--411},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1991},
MRCLASS = {52B05},
MRNUMBER = {1116365 (92h:52010)},
MRREVIEWER = {Bernd Kind},
}
@incollection {MR2077562,
AUTHOR = {Kaibel, Volker},
TITLE = {On the expansion of graphs of 0/1-polytopes},
BOOKTITLE = {The sharpest cut},
SERIES = {MPS/SIAM Ser. Optim.},
PAGES = {199--216},
PUBLISHER = {SIAM},
ADDRESS = {Philadelphia, PA},
YEAR = {2004},
MRCLASS = {05C50 (05C40 52B11 52B12 52B60 68W20)},
MRNUMBER = {2077562 (2005f:05101)},
MRREVIEWER = {Mark R. Jerrum},
}
@article{figiel1977dimension,
title={The dimension of almost spherical sections of convex bodies},
author={Figiel, Tadeusz and Lindenstrauss, Joram and Milman, Vitali D.},
journal={Acta Mathematica},
volume={139},
number={1},
pages={53--94},
year={1977},
publisher={Springer}
}
@book{Federer,
title = {Geometric Measure Theory},
author = {Federer, Herbert},
year = {1969},
publisher = {Springer},
}
@book {MR0201189,
AUTHOR = {Dantzig, George B.},
TITLE = {Linear programming and extensions},
PUBLISHER = {Princeton University Press},
ADDRESS = {Princeton, N.J.},
YEAR = {1963},
PAGES = {xvi+625},
MRCLASS = {90.50},
MRNUMBER = {0201189 (34 \#1073)},
MRREVIEWER = {P. L. Iv{\v{a}}nescu},
}
@incollection {MR0332165,
AUTHOR = {Klee, Victor and Minty, George J.},
TITLE = {How good is the simplex algorithm?},
BOOKTITLE = {Inequalities, III (Proc. Third Sympos.,
Univ. California, Los Angeles, Calif., 1969;
dedicated to the memory of Theodore S. Motzkin)},
PAGES = {159--175},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = 1972
}
@inproceedings{Friedmann:2011:SLB:2133036.2133055,
author = {Friedmann, Oliver and Hansen, Thomas Dueholm and Zwick, Uri},
title = {A subexponential lower bound for the random facet algorithm for parity games},
booktitle = {Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms},
series = {SODA '11},
year = {2011},
location = {San Francisco, California},
pages = {202--216},
numpages = {15},
url = {http://dl.acm.org/citation.cfm?id=2133036.2133055},
acmid = {2133055},
publisher = {SIAM},
}
@incollection {MR1661377,
AUTHOR = {Amenta, Nina and Ziegler, G{\"u}nter M.},
TITLE = {Deformed products and maximal shadows of polytopes},
BOOKTITLE = {Advances in discrete and computational geometry ({S}outh
{H}adley, {MA}, 1996)},
SERIES = {Contemp. Math.},
VOLUME = {223},
PAGES = {57--90},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1999},
MRCLASS = {52B05 (52B55 65D18)},
MRNUMBER = {1661377 (2000a:52019)},
MRREVIEWER = {P. McMullen},
}
@inproceedings{Kalai:1992:SRS:129712.129759,
author = {Kalai, Gil},
title = {A subexponential randomized simplex algorithm (extended abstract)},
booktitle = {Proceedings of the twenty-fourth annual ACM symposium on Theory of computing},
series = {STOC '92},
year = {1992},
isbn = {0-89791-511-9},
location = {Victoria, British Columbia, Canada},
pages = {475--482},
numpages = {8},
url = {http://doi.acm.org/10.1145/129712.129759},
doi = {10.1145/129712.129759},
acmid = {129759},
publisher = {ACM},
address = {New York, NY, USA},
}
@article {MR1407586,
AUTHOR = {Matou{\v{s}}ek, Ji{\v{r}}i and Sharir, Micha and Welzl, Emo},
TITLE = {A subexponential bound for linear programming},
JOURNAL = {Algorithmica},
FJOURNAL = {Algorithmica. An International Journal in Computer Science},
VOLUME = {16},
YEAR = {1996},
NUMBER = {4-5},
PAGES = {498--516},
ISSN = {0178-4617},
CODEN = {ALGOEJ},
MRCLASS = {90C08 (68Q25 68U05 90C27)},
MRNUMBER = {1407586 (97f:90052)},
DOI = {10.1007/s004539900062},
URL = {http://dx.doi.org/10.1007/s004539900062},
}
@book {MR868467,
AUTHOR = {Borgwardt, Karl-Heinz},
TITLE = {The simplex method: A probabilistic analysis},
SERIES = {Algorithms and Combinatorics: Study and Research Texts},
VOLUME = {1},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = {1987},
PAGES = {xii+268},
ISBN = {3-540-17096-0},
MRCLASS = {90C05},
MRNUMBER = {868467 (88k:90110)},
MRREVIEWER = {J{\"u}rgen K{\"o}hler},
}
@article {MR2145860,
AUTHOR = {Spielman, Daniel A. and Teng, Shang-Hua},
TITLE = {Smoothed analysis of algorithms: why the simplex algorithm
usually takes polynomial time},
JOURNAL = {J. ACM},
FJOURNAL = {Journal of the ACM},
VOLUME = {51},
YEAR = {2004},
NUMBER = {3},
PAGES = {385--463 (electronic)},
ISSN = {0004-5411},
MRCLASS = {90C05 (68W40 90C60)},
MRNUMBER = {2145860 (2006f:90029)},
MRREVIEWER = {Panos M. Pardalos},
DOI = {10.1145/990308.990310},
URL = {http://dx.doi.org/10.1145/990308.990310},
}
@Article{Khachiyan79,
author = {Leonid Genrikhovich Khachiyan},
title = {A polynomial algorithm in linear programming},
journal = {Doklady Akademii Nauk SSSR},
year = 1979,
volume = 244,
pages = {1093-1097}
}
@article {MR779900,
AUTHOR = {Karmarkar, Narendra},
TITLE = {A new polynomial-time algorithm for linear programming},
JOURNAL = {Combinatorica},
FJOURNAL = {Combinatorica. An International Journal of the J\'anos Bolyai
Mathematical Society},
VOLUME = {4},
YEAR = {1984},
NUMBER = {4},
PAGES = {373--395},
ISSN = {0209-9683},
CODEN = {COMBDI},
MRCLASS = {90C05},
MRNUMBER = {779900 (86i:90072)},
MRREVIEWER = {K. G. Murty},
DOI = {10.1007/BF02579150},
URL = {http://dx.doi.org/10.1007/BF02579150},
}
@incollection {MR780411,
AUTHOR = {Karmarkar, Narendra and Karp, Richard M.},
TITLE = {An efficient approximation scheme for the one-dimensional
bin-packing problem},
BOOKTITLE = {23rd {A}nnual {S}ymposium on {F}oundations of {C}omputer {S}cience
({C}hicago, {I}ll., 1982)},
PAGES = {312--320},
PUBLISHER = {IEEE},
ADDRESS = {New York},
YEAR = {1982},
MRCLASS = {68Q20 (68R05 90B35)},
MRNUMBER = {780411},
}
@inproceedings{Kelner:2006:RPS:1132516.1132524,
author = {Kelner, Jonathan A. and Spielman, Daniel A.},
title = {A randomized polynomial-time simplex algorithm for linear programming},
booktitle = {Proceedings of the thirty-eighth annual ACM symposium on Theory of computing},
series = {STOC '06},
year = {2006},
isbn = {1-59593-134-1},
location = {Seattle, WA, USA},
pages = {51--60},
numpages = {10},
url = {http://doi.acm.org/10.1145/1132516.1132524},
doi = {10.1145/1132516.1132524},
acmid = {1132524},
publisher = {ACM},
address = {New York, NY, USA},
}
@article{Bertsimas:2004:SCP:1008731.1008733,
author = {Bertsimas, Dimitris and Vempala, Santosh},
title = {Solving convex programs by random walks},
journal = {J. ACM},
issue_date = {July 2004},
volume = {51},
number = {4},
month = jul,
year = {2004},
issn = {0004-5411},
pages = {540--556},
numpages = {17},
url = {http://doi.acm.org/10.1145/1008731.1008733},
doi = {10.1145/1008731.1008733},
acmid = {1008733},
publisher = {ACM},
address = {New York, NY, USA},
keywords = {Convex programs, polynomial time, random walks},
}
@article {MR727410,
AUTHOR = {Lenstra, Jr., Hendrik Willem},
TITLE = {Integer programming with a fixed number of variables},
JOURNAL = {Math. Oper. Res.},
FJOURNAL = {Mathematics of Operations Research},
VOLUME = {8},
YEAR = {1983},
NUMBER = {4},
PAGES = {538--548},
ISSN = {0364-765X},
MRCLASS = {90C10},
MRNUMBER = {727410 (86f:90106)},
DOI = {10.1287/moor.8.4.538},
URL = {http://dx.doi.org/10.1287/moor.8.4.538},
}
@article {MR906415,
AUTHOR = {Kannan, Ravi},
TITLE = {Minkowski's convex body theorem and integer programming},
JOURNAL = {Math. Oper. Res.},
FJOURNAL = {Mathematics of Operations Research},
VOLUME = {12},
YEAR = {1987},
NUMBER = {3},
PAGES = {415--440},
ISSN = {0364-765X},
MRCLASS = {90C10 (68Q25)},
MRNUMBER = {906415 (89c:90078)},
MRREVIEWER = {Uwe Zimmermann},
DOI = {10.1287/moor.12.3.415},
URL = {http://dx.doi.org/10.1287/moor.12.3.415},
}
@inproceedings {MR2120363,
AUTHOR = {Ajtai, Mikl{\'o}s and Kumar, Ravi and Sivakumar, D.},
TITLE = {A sieve algorithm for the shortest lattice vector problem},
BOOKTITLE = {Proceedings of the {T}hirty-{T}hird {A}nnual {ACM} {S}ymposium
on {T}heory of {C}omputing},
PAGES = {601--610 (electronic)},
PUBLISHER = {ACM},
ADDRESS = {New York},
YEAR = {2001},
MRCLASS = {68W20 (68Q25 94B40)},
MRNUMBER = {2120363 (2005k:68224)},
DOI = {10.1145/380752.380857},
URL = {http://dx.doi.org/10.1145/380752.380857},
}
@article {MR2508524,
AUTHOR = {Bl{\"o}mer, Johannes and Naewe, Stefanie},
TITLE = {Sampling methods for shortest vectors, closest vectors and
successive minima},
JOURNAL = {Theoret. Comput. Sci.},
FJOURNAL = {Theoretical Computer Science},
VOLUME = {410},
YEAR = {2009},
NUMBER = {18},
PAGES = {1648--1665},
ISSN = {0304-3975},
CODEN = {TCSDI},
MRCLASS = {68Q25 (11H06 68W25)},
MRNUMBER = {2508524 (2010e:68081)},
MRREVIEWER = {S. V. Nagaraj},
DOI = {10.1016/j.tcs.2008.12.045},
URL = {http://dx.doi.org/10.1016/j.tcs.2008.12.045},
}
@incollection {MR2743283,
AUTHOR = {Micciancio, Daniele and Voulgaris, Panagiotis},
TITLE = {A deterministic single exponential time algorithm for most
lattice problems based on {V}oronoi cell computations
[extended abstract]},
BOOKTITLE = {S{TOC}'10---{P}roceedings of the 2010 {ACM} {I}nternational
{S}ymposium on {T}heory of {C}omputing},
PAGES = {351--358},
PUBLISHER = {ACM},
ADDRESS = {New York},
YEAR = {2010},
MRCLASS = {68Q25 (68P25)},
MRNUMBER = {2743283},
}
@inproceedings{DPV10,
author = {Daniel Dadush and
Chris Peikert and
Santosh Vempala},
title = {Enumerative Lattice Algorithms in any Norm Via M-ellipsoid
Coverings},
booktitle = {FOCS},
year = {2011},
pages = {580-589},
ee = {http://dx.doi.org/10.1109/FOCS.2011.31},
crossref = {DBLP:conf/focs/2011},
bibsource = {DBLP, http://dblp.uni-trier.de}
}
@proceedings{DBLP:conf/focs/2011,
editor = {Rafail Ostrovsky},
title = {IEEE 52nd Annual Symposium on Foundations of Computer Science,
FOCS 2011, Palm Springs, CA, USA, October 22-25, 2011},
booktitle = {FOCS},
publisher = {IEEE},
year = {2011},
isbn = {978-1-4577-1843-4},
ee = {http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6108120},
bibsource = {DBLP, http://dblp.uni-trier.de}
}
@article {MR2433777,
AUTHOR = {F{\"u}redi, Zolt{\'a}n and Kang, Jeong-Hyun},
TITLE = {Covering the {$n$}-space by convex bodies and its chromatic
number},
JOURNAL = {Discrete Math.},
FJOURNAL = {Discrete Mathematics},
VOLUME = {308},
YEAR = {2008},
NUMBER = {19},
PAGES = {4495--4500},
ISSN = {0012-365X},
CODEN = {DSMHA4},
MRCLASS = {52C17 (05C15 05C62)},
MRNUMBER = {2433777 (2009c:52031)},
MRREVIEWER = {Tiong Seng Tay},
DOI = {10.1016/j.disc.2007.08.048},
URL = {http://dx.doi.org/10.1016/j.disc.2007.08.048},
}
@techreport{vEB81,
author= {van Emde Boas, Peter},
title = {Another \textsc{NP}-Complete Problem and the Complexity of Computing Short Vectors in a Lattice},
institution = {Mathematische Instituut, University of Amsterdam },
number = {81-04},
year = {1981}
}
@article {er61,
AUTHOR = {Erd{\H{o}}s, Paul and Rogers, Claude Ambrose},
TITLE = {Covering space with convex bodies},
JOURNAL = {Acta Arith.},
FJOURNAL = {Polska Akademia Nauk. Instytut Matematyczny. Acta Arithmetica},
VOLUME = {7},
YEAR = {1961/1962},
PAGES = {281--285},
ISSN = {0065-1036},
MRCLASS = {52.45},
MRNUMBER = {0149373 (26 \#6863)},
MRREVIEWER = {E. G. Straus},
}
@inproceedings{aks02,
author={Ajtai, Mikl{\'o}s and Kumar, Ravi and Sivakumar, D.},
booktitle={Computational Complexity, 2002. Proceedings. 17th IEEE Annual Conference on},
title={Sampling short lattice vectors and the closest lattice vector problem},
year={2002},
volume={},
number={},
pages={41 -45},
keywords={SVP algorithm;Turing reduction;closest lattice vector problem;complexity;deterministic algorithm;randomized algorithm;shortest lattice vector problem;subroutine;time bound;computational complexity;deterministic algorithms;randomised algorithms;subroutines;},
doi={10.1109/CCC.2002.1004339},
ISSN={},
}
@phdthesis{aroraPhD,
author = {Arora, Sanjeev},
title = {Probabilistic checking of proofs and the hardness of approximation problems},
school = {UC Berkeley},
year = {1994}
}
@article {dkrs03,
AUTHOR = {Dinur, Irit and Kindler, Guy and Raz, Ran and Safra, Shmuel},
TITLE = {Approximating {CVP} to within almost-polynomial factors is
{NP}-hard},
JOURNAL = {Combinatorica},
FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
the Theory of Computing},
VOLUME = {23},
YEAR = {2003},
NUMBER = {2},
PAGES = {205--243},
ISSN = {0209-9683},
MRCLASS = {68Q17},
MRNUMBER = {2001908 (2004h:68046)},
MRREVIEWER = {Johan H{\aa}stad},
DOI = {10.1007/s00493-003-0019-y},
URL = {http://dx.doi.org/10.1007/s00493-003-0019-y},
}
@article {MR677658,
AUTHOR = {Karp, Richard M. and Papadimitriou, Christos H.},
TITLE = {On linear characterizations of combinatorial optimization
problems},
JOURNAL = {SIAM J. Comput.},
FJOURNAL = {SIAM Journal on Computing},
VOLUME = {11},
YEAR = {1982},
NUMBER = {4},
PAGES = {620--632},
ISSN = {0097-5397},
CODEN = {SMJCAT},
MRCLASS = {90C10 (90C05)},
MRNUMBER = {677658 (83k:90070)},
DOI = {10.1137/0211053},
URL = {http://dx.doi.org/10.1137/0211053},
}
@techreport{PadbergRao81,
author = {Padberg, Manfred Wilhelm and Rao, Mendu Rammohan},
title = {The {R}ussian method for linear inequalities {III}: {B}ounded integer programming},
institution = {INRIA},
year = 1981,
type = {Rapports de Recherche},
number = {78}
}
@article {MR625550,
AUTHOR = {Gr{\"o}tschel, Martin and Lov{\'a}sz, L{\'a}szl{\'o} and Schrijver, Alexander},
TITLE = {The ellipsoid method and its consequences in combinatorial
optimization},
JOURNAL = {Combinatorica},
FJOURNAL = {Combinatorica. An International Journal of the J\'anos Bolyai
Mathematical Society},
VOLUME = {1},
YEAR = {1981},
NUMBER = {2},
PAGES = {169--197},
ISSN = {0209-9683},
CODEN = {COMBDI},
MRCLASS = {90C05 (05Cxx)},
MRNUMBER = {625550 (84a:90044)},
DOI = {10.1007/BF02579273},
URL = {http://dx.doi.org/10.1007/BF02579273},
}
@article {MR2386164,
AUTHOR = {Dunagan, John and Vempala, Santosh},
TITLE = {A simple polynomial-time rescaling algorithm for solving
linear programs},
JOURNAL = {Math. Program.},
FJOURNAL = {Mathematical Programming. A Publication of the Mathematical
Programming Society},
VOLUME = {114},
YEAR = {2008},
NUMBER = {1, Ser. A},
PAGES = {101--114},
ISSN = {0025-5610},
MRCLASS = {90C05 (68Q32 68T05)},
MRNUMBER = {2386164 (2009b:90061)},
DOI = {10.1007/s10107-007-0095-7},
URL = {http://dx.doi.org/10.1007/s10107-007-0095-7},
}
@incollection {MR1491097,
AUTHOR = {Ball, Keith},
TITLE = {An elementary introduction to modern convex geometry},
BOOKTITLE = {Flavors of geometry},
SERIES = {Math. Sci. Res. Inst. Publ.},
VOLUME = {31},
PAGES = {1--58},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {1997},
MRCLASS = {52-02 (46B07 52A21 52A40)},
MRNUMBER = {1491097 (99f:52002)},
MRREVIEWER = {Peter M. Gruber},
}
@article {MR0124818,
AUTHOR = {Gr{\"u}nbaum, Branko},
TITLE = {Partitions of mass-distributions and of convex bodies by
hyperplanes. },
JOURNAL = {Pacific J. Math.},
FJOURNAL = {Pacific Journal of Mathematics},
VOLUME = {10},
YEAR = {1960},
PAGES = {1257--1261},
ISSN = {0030-8730},
MRCLASS = {53.90 (52.40)},
MRNUMBER = {0124818 (23 \#A2128)},
MRREVIEWER = {H. G. Eggleston},
}
@InProceedings{ER10,
author = {Friedrich Eisenbrand and Thomas Rothvo\ss},
title = {{EDF}-schedulability of synchronous periodic task systems is {coNP}-hard},
booktitle = {ACM-SIAM Symposium on Discrete Algorithms (SODA 10)},
pages = {1227-1234},
year = 2010
}
@ARTICLE{Lagarias85,
AUTHOR = {Jeffrey Clark Lagarias},
JOURNAL = {SIAM J. Computing},
NUMBER = {1},
PAGES = {196 -- 209},
TITLE = {The computational complexity of simultaneous
{D}iophantine approximation problems},
VOLUME = {14},
YEAR = {1985}
}
@article {MR2312001,
AUTHOR = {Verdoolaege, Sven and Seghir, Rachid and Beyls, Kristof and
Loechner, Vincent and Bruynooghe, Maurice},
TITLE = {Counting integer points in parametric polytopes using
{B}arvinok's rational functions},
JOURNAL = {Algorithmica},
FJOURNAL = {Algorithmica. An International Journal in Computer Science},
VOLUME = {48},
YEAR = {2007},
NUMBER = {1},
PAGES = {37--66},
ISSN = {0178-4617},
CODEN = {ALGOEJ},
MRCLASS = {52C07 (05A15 68N20 90C10)},
MRNUMBER = {2312001 (2008h:52019)},
MRREVIEWER = {Kevin Woods},
DOI = {10.1007/s00453-006-1231-0},
URL = {http://dx.doi.org/10.1007/s00453-006-1231-0},
}
@book {MR2445243,
AUTHOR = {Hardy, Godfrey Harold and Wright, Edward Maitland},
TITLE = {An introduction to the theory of numbers},
EDITION = {Sixth},
NOTE = {Revised by D. R. Heath-Brown and J. H. Silverman,
With a foreword by Andrew Wiles},
PUBLISHER = {Oxford University Press},