Sample
Sparse integer programming is FPT (and compact form) (with Martin Koutecky), Bulletin of the European Association for Theoretical Computer Science, 134:69--71, 2021.
An algorithmic theory of integer programming (with Friedrich Eisenbrand, Christoph Hunkenschroder, Kim-Manuel Klein, Martin Koutecky and Asaf Levin), arXiv:1904.01361, 2019.
Hypergraphic degree sequences are hard (and compact form) (with Antoine Deza, Asaf Levin and Syed M. Meesum), Bulletin of the European Association for Theoretical Computer Science, 127:63--64, 2019.
A parameterized strongly polynomial algorithm for block structured integer programs (with Martin Koutecky and Asaf Levin), Proceedings of ICALP 2018 (International Colloquium on Automata, Languages, and Programming), Leibniz International Proceedings in Informatics, 107-85:1--14, 2018.
N-fold integer programming in cubic time (hence multiway tables are fixed-parameter tractable) (with Raymond Hemmecke and Lyubov Romanchuk), Mathematical Programming, 137:325--341, 2013.
Approximate nonlinear optimization over weighted independence systems (with Jon Lee and Robert Weismantel), SIAM Journal on Discrete Mathematics, 23:1667--1681, 2009.
N-fold integer programming (selected for the 10th Anniversary Issue of Discrete Optimization) (with Jesus De Loera, Raymond Hemmecke and Robert Weismantel), Discrete Optimization, 5:231--241, 2008.
Nonlinear bipartite matching (with Yael Berstein), Discrete Optimization, 5:53--65, 2008.
All linear and integer programs are slim 3-way transportation programs (with Jesus De Loera), SIAM Journal on Optimization, 17:806--821, 2006.
Convex combinatorial optimization (with Uriel G. Rothblum), Discrete and Computational Geometry, 32:549--566, 2004.
The Hilbert zonotope and a polynomial time algorithm for universal Grobner bases (with Eric Babson and Rekha Thomas), Advances in Applied Mathematics, 30:529--544, 2003.
Cutting corners (and figure of corner polytopes) (with Bernd Sturmfels), Advances in Applied Mathematics, 23:29--48, 1999.
A polynomial time algorithm for shaped partition problems (with Frank Hwang and Uriel G. Rothblum), SIAM Journal on Optimization, 10:70--81, 1999.
Colourful linear programming and its relatives (with Imre Barany), Mathematics of Operations Research, 22:550--567, 1997.
On the diameter of convex polytopes (with Peter Kleinschmidt), Discrete Mathematics, 102:75--77, 1992.
Near complete list
Degree sequence optimization and extremal degree enumerators, arXiv:2404.02551, 2024.
Kissing polytopes (with A. Deza, S. Pokutta, L. Pournin), arXiv:2305.18597, 2023.
Asymptotic behavior of Markov complexity of matrices (with A. Thoma, M. Vladoiu), Journal of Pure and Applied Algebra, 228:107589 (16 pages), 2024, online.
On supmodular matrices, Linear and Multilinear Algebra, 2023, online.
Reducibility bounds of objective functions over the integers (with F. Eisenbrand, C. Hunkenschroder, K.-M. Klein, M. Koutecky, A. Levin), Operations Research Letters, 51:595--598, 2023, online.
Degree sequence optimization in bounded treewidth, Optimization Letters, 17:1127--1132, 2023, online.
Separable and equatable hypergraphs (with D. Deza), Discrete Applied Mathematics, 332:170--179, 2023, online.
High multiplicity n-fold IP via configuration LP (with D. Knop, M. Koutecky, A. Levin, M. Mnich), Mathematical Programming, 200:199--227, 2023.
The complexity of vector partition, Vietnam Journal of Mathematics, 50:707--718, 2022, Selected for Vietnam Journal of Mathematics Editors' Choice.
Matching orderable and separable hypergraphs, Optimization Letters, 16:1393--1401, 2022.
Approximate separable multichoice optimization over monotone systems (with M. Koutecky, A. Levin, S.M. Meesum), Discrete Optimization, 44:100629 (15 pages), 2022.
Sparse Integer Programming is FPT (with M. Koutecky), Bulletin of the European Association for Theoretical Computer Science, 134:69--71, 2021.
Parameterized complexity of configuration integer programs (with D. Knop, M. Koutecky, A. Levin, M. Mnich), Operations Research Letters, 49:908--913, 2021.
Optimization over Young diagrams, Journal of Algebraic Combinatorics, 54:689--692, 2021.
Uniform and monotone line sum optimization (with M. Koutecky), Discrete Applied Mathematics, 298:165--170, 2021.
On line sum optimization, Linear Algebra and its Applications, 610:474--479, 2021.
Optimization over degree sequences of graphs (with G. Deza), Discrete Applied Mathematics, 296:2--8, 2021.
On degree sequences optimization, Operations Research Letters, 48:840--843, 2020.
An algorithmic theory of integer programming (with F. Eisenbrand, C. Hunkenschroder, K.M. Klein, M. Koutecky, A. Levin), arXiv:1904.01361, 2019.
Hypergraphic degree sequences are hard (with A. Deza, A. Levin, S.M. Meesum), Bulletin of the European Association for Theoretical Computer Science, 127:63--64, 2019.
Parameterized shifted combinatorial optimization (with, J. Gajarsky, P. Hlineny, M. Koutecky), Journal of Computer and System Sciences, 99:53--71, 2019.
On the complexity of toric ideals (with D. Cifuentes), arXiv:1902.01484, 2019.
Multitype integer monoid optimization and applications (with D. Knop, M. Koutecky, A. Levin, M. Mnich), arXiv:1909.07326, 2019.
Optimization over degree sequences (with A. Deza, A. Levin, S.M. Meesum), SIAM Journal on Discrete Mathematics, 32:2067--2079, 2018.
Primitive zonotopes (with A. Deza, G. Manoussakis), Discrete and Computational Geometry, 60:27--39, 2018.
A parameterized strongly polynomial algorithm for block structured integer programs (with M. Koutecky, A. Levin), in: International Colloquium on Automata, Languages, and Programming, 45th ICALP Proceedings, Leibniz International Proceedings in Informatics, 107-85:1--14, Schloss Dagstuhl, 2018.
Small primitive zonotopes (with A. Deza, G. Manoussakis), in: Discrete Geometry and Symmetry, Springer Proceedings in Mathematics and Statistics, 234:87--107, Springer, 2018.
Huge tables and multicommodity flows are fixed-parameter tractable via unimodular integer Caratheodory, Journal of Computer and System Sciences, 83:207--214, 2017.
On nonlinear multi-covering problems (with R. Cohen, M. Gonen, A. Levin), Journal of Combinatorial Optimization, 33:645--659, 2017.
Parameterized shifted combinatorial optimization (with, J. Gajarsky, P. Hlineny, M. Koutecky), in: Proceedings of the 23rd Annual International Computing and Combinatorics Conference (2017), Lecture Notes in Computer Science, 10392:224--236, Springer, 2017.
Shifted matroid optimization (with A. Levin), Operations Research Letters, 44:535--539, 2016.
Efficient solutions for weight-balanced partitioning problems (with S. Borgwardt), Discrete Optimization, 21:71--84, 2016.
Huge unimodular n-fold programs (with P. Sarrabezolles), SIAM Journal on Discrete Mathematics, 29:2277--2283, 2015.
The unimodular intersection problem (with V. Kaibel, P. Sarrabezolles), Operations Research Letters, 43:592--594, 2015.
On the complexity of Hilbert refutations for partition (with S. Margulies, D.V. Pasechnik), Journal of Symbolic Computation, 66:70--83, 2015.
Some efficiently solvable problems over integer partition polytopes (with V. Shlyk), Discrete Applied Mathematics, 180:135--140, 2015.
Robust integer programming, Operations Research Letters, 42:558--560, 2014.
Huge multiway table problems, Discrete Optimization, 14:72--77, 2014.
Convex integer optimization by constantly many linear counterparts (with M. Rozenblit), Linear Algebra and its Applications, 447:88--109, 2014.
N-fold integer programming in cubic time (with R. Hemmecke, L. Romanchuk), Mathematical Programming, 137:325--341, 2013, Winner of the 2011 ORSIS Abraham Mechrez Prize for Best Student Paper.
The quadratic Graver cone, quadratic integer minimization, and extensions (with J. Lee, L. Romanchuk, R. Weismantel), Mathematical Programming, 136:301--323, 2012.
Minimizing Lipschitz-continuous strongly convex functions over integer points in polyhedra (with M. Baes, A. Del Pia, Y. Nesterov, R. Weismantel), Mathematical Programming, 134:305--322, 2012, Special volume of invited research articles for the 21st Triannual International Symposium on Mathematical Programming.
Theory and applications of n-fold integer programming, in: Mixed Integer Nonlinear Programming (edited by J. Lee, S. Leyffer), The IMA Volumes in Mathematics and its Applications, Volume 154, 559--593, Springer, 2012.
A polynomial oracle-time algorithm for convex integer minimization (with R. Hemmecke, R. Weismantel), Mathematical Programming, 126:97--117, 2011.
Intractability of approximate multi-dimensional nonlinear optimization on independence systems (with J. Lee, R. Weismantel) , Discrete Mathematics, 311:780--783, 2011.
N-fold integer programming and nonlinear multi-transshipment (with R. Hemmecke, R. Weismantel), Optimization Letters, 5:13--25, 2011.
Generating uniform random vectors over a simplex with implications to the volume of a certain polytope and to multivariate extremes (with I. Weissman), Annals of Operations Research, 189:331--342, 2011.
Convex discrete optimization, in: Combinatorial Optimization: Methods and Applications (edited by V. Chvatal), NATO Science for Peace and Security Series, Volume 31, 183--228, IOS Press, 2011.
Polynomial time primal integer programming via Graver bases, in: Encyclopedia of Operations Research and Management Science, 14 pages, Wiley, 2011.
Accuracy certificates for computational problems with convex structure (with A. Nemirovski, U.G. Rothblum), Mathematics of Operations Research, 35:52--78, 2010.
Minimal average degree aberration and the state polytope for experimental designs (with Y. Berstein, H. Maruri-Aguilar, E. Riccomagno, H. Wynn), Annals of the Institute of Statistical Mathematics, 62:673--698, 2010.
Parametric nonlinear discrete optimization over well-described sets and matroid intersections (with Y. Berstein, J. Lee, R. Weismantel), Mathematical Programming, 124:233--253, 2010.
Approximate nonlinear optimization over weighted independence systems (with J. Lee, R. Weismantel) , SIAM Journal on Discrete Mathematics, 23:1667--1681, 2009.
Graphs of transportation polytopes (with J. De Loera, E.D. Kim, F. Santos), Journal of Combinatorial Theory Series A, 116:1306--1325, 2009.
The Graver complexity of integer programming (with Y. Berstein), Annals of Combinatorics, 13:289--296, 2009.
Expressing combinatorial optimization problems by systems of polynomial equations and the Nullstellensatz (with J. De Loera, J. Lee, S. Margulies), Combinatorics, Probability and Computing, 18:551--582, 2009, Winner of the 2010 INFORMS Computing Society Prize.
Two graph isomorphism polytopes, Discrete Mathematics, 309:2934--2936, 2009.
Convex integer maximization via Graver bases (with J. De Loera, R. Hemmecke, S. Onn, U.G. Rothblum, R. Weismantel) , Journal of Pure and Applied Algebra, 213:1569--1577, 2009.
Nonlinear optimization over a weighted independence system (with J. Lee, R. Weismantel), in: Algorithmic Aspects in Information and Management, AAIM 2009 Proceedings (edited by A. Goldberg, Y. Zhou), Lecture Notes in Computer Science, 5564:251--264, Springer, 2009.
Convex discrete optimization, in: Encyclopedia of Optimization (edited by C.A. Floudas, P.M. Pardalos), 513--550, Springer, 2009.
Nash-equilibria and n-fold integer programming (with R. Hemmecke, R. Weismantel), arXiv:0903.4577, 2009.
On test sets for nonlinear integer maximization (with J. Lee, R. Weismantel), Operations Research Letters, 36:439--443, 2008.
Nonlinear matroid optimization and experimental design (with Y. Berstein, J. Lee, H. Maruri-Aguilar, E. Riccomagno, R. Weismantel, H. Wynn), SIAM Journal on Discrete Mathematics, 22:901--919, 2008.
N-fold integer programming (with J. De Loera, R. Hemmecke, R. Weismantel), Discrete Optimization, 5:231--241, 2008, Selected for the 10th Anniversary Issue of Discrete Optimization.
Nonlinear bipartite matching (with Y. Berstein), Discrete Optimization, 5:53--65, 2008, Winner of the 2008 ORSIS Abraham Mechrez Prize for Best Student Paper.
The convex dimension of a graph (with N. Halman, U.G. Rothblum), Discrete Applied Mathematics, 155:1373--1383, 2007.
The use of edge-directions and linear programming to enumerate vertices (with U.G. Rothblum), Journal of Combinatorial Optimization, 14:153--164, 2007.
All linear and integer programs are slim 3-way transportation programs (with J. De Loera), SIAM Journal on Optimization, 17:806--821, 2006.
Permutohedra and minimal matrices (with E. Vallejo), Linear Algebra and its Applications, 412:471--489, 2006.
Markov bases of three-way tables are arbitrarily complicated (with J. De Loera), Journal of Symbolic Computation, 41:173--181, 2006.
Entry uniqueness in margined tables, in: Privacy in Statistical Databases, PSD 2006 Proceedings (edited by J. Domingo-Ferrer, L. Franconi), Lecture Notes in Computer Science, 4302:94--101, Springer, 2006.
Edge-directions of standard polyhedra with applications to network flows (with U.G. Rothblum, Y. Tangir), Journal of Global Optimization, 33:109--122, 2005.
The complexity of three-way statistical tables (with J. De Loera), SIAM Journal on Computing, 33:819--836, 2004.
Nowhere-zero flow polynomials, Journal of Combinatorial Theory Series A, 108:205--215, 2004.
The minimum number of edge-directions of a convex polytope (with R. Pinchasi), Journal of Combinatorial Theory Series A, 107:147--151, 2004.
Convex combinatorial optimization (with U.G. Rothblum), Discrete and Computational Geometry, 32:549--566, 2004, Winner of the 2005 ORSIS Prize for Best Research Paper in Operations Research.
All rational polytopes are transportation polytopes and all polytopal integer sets are contingency tables (with J. De Loera), in: Integer Programming and Combinatorial Optimization, 10th IPCO Proceedings (edited by D. Bienstock, G. Nemhauser), Lecture Notes in Computer Science, 3064:338--351, Springer, 2004.
Convex matroid optimization, SIAM Journal on Discrete Mathematics, 17:249--253, 2003.
The Hilbert zonotope and a polynomial time algorithm for universal Grobner bases (with E. Babson, R. Thomas), Advances in Applied Mathematics, 30:529--544, 2003.
An adaptive algorithm for vector partitioning (with K. Fukuda, V. Rosta), Journal of Global Optimization, 25:305--319, 2003.
Social network coordination and graph routing (with E. Sperber), Networks, 41:44--50, 2003.
Automated transformations for PDE systems with applications to multigrid solvers (with Y. Gil, Z. Gutterman, I. Yavneh), SIAM Journal on Scientific Computing, 24:886--904, 2002.
Momentopes, the complexity of vector partitioning, and Davenport Schinzel sequences (with S. Aviran), Discrete and Computational Geometry, 27:409--417, 2002.
Solitaire lattices (with A. Deza), Graphs and Combinatorics, 18:227--243, 2002.
Vertex characterization of partition polytopes of bipartitions and of planar point sets (with S. Aviran, N. Lev-Tov, U.G. Rothblum), Discrete Applied Mathematics, 124:1--15, 2002.
The Radon-split and the Helly-core of a point configuration, Journal of Geometry, 72:157--162, 2001.
The vector partition problem for convex objective functions (with L.J. Schulman), Mathematics of Operations Research, 26:583--590, 2001.
Explicit solution of partitioning problems over a 1-dimensional parameter space (with F.K. Hwang, U.G. Rothblum), Naval Research Logistics, 47:531--540, 2000.
A combinatorial approach to the solitaire game (with D. Avis, A. Deza), Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E83-A:656--661, 2000.
Linear shaped partition problems (with F.K. Hwang, U.G. Rothblum), Operations Research Letters, 26:159--163, 2000.
A polynomial time algorithm for shaped partition problems (with F.K. Hwang, U.G. Rothblum), SIAM Journal on Optimization, 10:70--81, 1999.
Cutting Corners (with B. Sturmfels), Advances in Applied Mathematics, 23:29--48, 1999.
Separable partitions (with N. Alon), Discrete Applied Mathematics, 91:39--51, 1999, Selected for Discrete Applied Mathematics Editors' Choice.
Odd central square Solitaire (with A. Deza), Kokyuroku, 1114:96--105, Research Institute for Mathematical Sciences (RIMS), Kyoto University, 1999.
Representations and characterizations of vertices of bounded-shape partition-polytopes (with F.K. Hwang, U.G. Rothblum) , Linear Algebra and its Applications, 278:263--284, 1998.
Determination of social laws for multi-agent mobilization (with M. Tennenholtz), Artificial Intelligence, 95:155--167, 1997.
Strongly signable and partitionable posets, European Journal of Combinatorics, 18:921--938, 1997.
Colourful linear programming and its relatives (with I. Barany), Mathematics of Operations Research, 22:550--567, 1997.
A colorful determinantal identity, a conjecture of Rota, and Latin squares, The American Mathematical Monthly, 104:156--159, 1997.
Caratheodory's theorem: colourful and applicable (with I. Barany), in: Bolyai Society Mathematical Studies (edited by I. Barany, K. Boroczky), 6:11--21, North-Holland, 1997.
Signable posets and partitionable simplicial complexes (with P. Kleinschmidt), Discrete and Computational Geometry, 15:443--466, 1996.
Colourful linear programming (with I. Barany), in: Integer Programming and Combinatorial Optimization, 5th IPCO Proceedings (edited by W.H. Cunningham, S.T. McCormick, M. Queyranne), Lecture Notes in Computer Science, 1084:1--15, Springer, 1996.
Lattice-free polytopes and their diameter (with M. Deza), Discrete and Computational Geometry, 13:59--75, 1995.
Oriented matroid polytopes and polyhedral cone fans are signable (with P. Kleinschmidt), in: Integer Programming and Combinatorial Optimization, 4th IPCO Proceedings (edited by E. Balas, J. Clausen), Lecture Notes in Computer Science, 920:198--211, Springer, 1995.
A quantitative Steinitz' theorem (with B. Sturmfels), Beitrage zur Algebra und Geometrie, 35:125--129, 1994.
Hilbert series of group representations and Grobner bases for generic modules, Journal of Algebraic Combinatorics, 3:187--206, 1994.
A note on lattice simplices and toric varieties (with B. Sturmfels), American Journal of Mathematics, 116:1337--1339, 1994.
Approximating oracle machines for combinatorial optimization, SIAM Journal on Optimization, 4:142--145, 1994.
Geometry, complexity, and combinatorics of permutation polytopes, Journal of Combinatorial Theory Series A, 64:31--49, 1993.
On the diameter of convex polytopes (with P. Kleinschmidt), Discrete Mathematics, 102:75--77, 1992.
On the geometry and computational complexity of Radon partitions in the integer lattice, SIAM Journal on Discrete Mathematics, 4:436--447, 1991.
On the Radon number of the integer lattice, in: Integer Programming and Combinatorial Optimization, 1st IPCO Proceedings (edited by R. Kannan, W.R. Pulleyblank), 385--396, 1990.