An algorithmic theory of integer programming

(with Friedrich Eisenbrand, Christoph Hunkenschroder,
Kim-Manuel Klein, Martin Koutecky and Asaf Levin)

Optimization over Degree Sequences of Graphs

(with Gabriel Deza)

On the complexity of toric ideals

(with Diego Cifuentes)

Approximate separable multichoice optimization over monotone systems

(with Martin Koutecky, Asaf Levin and Syed M. Meesum)

Parameterized shifted combinatorial optimization

(with Jakub Gajarsky, Petr Hlineny and Martin Koutecky)

*Journal of Computer and Systems Sciences*, 99:53--71, 2019.

Optimization over degree sequences
(in particular
hypergraphic degree sequences are hard
and
compact form)

(with Antoine Deza, Asaf Levin and Syed M. Meesum)

*SIAM Journal on Discrete Mathematics*,
*32:2067--2079, 2018.*

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),
Prague*

*Leibniz International Proceedings in Informatics*, 107-85:1--14, 2018
(preliminary full version).

Primitive zonotopes

(with Antoine Deza and George Manoussakis),
*Discrete and Computational Geometry*, 60:27--39, 2018.

Parameterized shifted combinatorial optimization

(with Jakub Gajarsky, Petr Hlineny and Martin Koutecky)

*Proceedings of COCOON 2017
(Computing and Combinatorics Conference), Hong Kong*

*Lecture Notes in Computer Science*, 10392:224--236, 2017.

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 Reuven Cohen, Mira Gonen and Asaf Levin),
*Journal of Combinatorial Optimization*, 33:645-659, 2017.

Shifted matroid optimization

(with Asaf Levin),
*Operations Research Letters*, 44:535-539, 2016.

Efficient solutions for weight-balanced partitioning problems

(with Steffen Borgwardt),
*Discrete Optimization*, 21:71-84, 2016.

Huge unimodular n-fold programs

(with Pauline Sarrabezolles),
*SIAM Journal on Discrete Mathematics*, 29:2277-2283, 2015.

The unimodular intersection problem

(with Volker Kaibel and Pauline Sarrabezolles),
*Operations Research Letters*, 43:592-594, 2015.

On the complexity of Hilbert refutations for Partition

(with Susan Margulies and Dmitrii Pasechnik),
*Journal of Symbolic Computation*, 66:70-83, 2015.

Some efficiently solvable problems over integer partition polytopes

(with Vladimir Shlyk),
*Discrete Applied Mathematics*, 180:135-140, 2015.

Huge multiway table problems

*Discrete Optimization*, 14:72-77, 2014.

Robust integer programming

*Operations Research Letters*, 42:558-560, 2014.

Convex integer optimization by constantly many linear counterparts

(with Michal Melamed),
*Linear Algebra and its Applications*, 447:88--109, 2014.

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.

The quadratic Graver cone, quadratic integer minimization, and extensions

(with Jon Lee, Lyubov Romanchuk and Robert Weismantel),
*Mathematical Programming*, 136:301--323, 2012.

Minimizing Lipschitz-continuous strongly
convex functions over integer points in polytopes

(with Michel Baes, Alberto Del Pia, Yurii Nesterov and Robert Weismantel),
*Mathematical Programming*, 134:305--322, 2012.

Theory and applications of n-fold integer programming

The IMA Volumes in Mathematics and its Applications,
Mixed Integer Nonlinear Programming,
154:559--593, 2012, Springer.

A polynomial oracle-time algorithm for convex integer minimization

(with Raymond Hemmecke and Robert Weismantel),
*Mathematical Programming*, 126: 97--117, 2011.

Intractability of approximate multi-dimensional nonlinear optimization on independence systems

(with Jon Lee and Robert Weismantel),
*Discrete Mathematics*, 311:780--783, 2011.

N-fold integer programming and nonlinear multi-transshipment

(with Raymond Hemmecke and Robert 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 Ishay Weissman),
*Annals of Operations Research*, 189:331--342, 2011.

Parametric nonlinear discrete optimization
over well-described sets and matroid intersections

(with Yael Berstein, Jon Lee and Robert Weismantel),
*Mathematical Programming*, 124:233--253, 2010.

Accuracy certificates for computational problems with convex structure

(with Arkadi Nemirovski and Uriel Rothblum),
*Mathematics of Operations Research*, 35:52--78, 2010.

Minimal average degree aberration and the state polytope for experimental designs

(with Yael Berstein, Hugo Maruri-Aguilar, Eva Riccomagno and Henry Wynn),
*Annals of the Institute of Statistical Mathematics*, 62:673--698, 2010.

Approximate nonlinear optimization over weighted independence systems

(with Jon Lee and Robert Weismantel),
*SIAM Journal on Discrete Mathematics*, 23:1667--1681, 2009.

The Graver complexity of integer programming

(with Yael Berstein),
*Annals of Combinatorics*, 13:289--296, 2009.

Nonlinear optimization over a weighted independence system
(also related
slides)

(with Jon Lee and Robert Weismantel),
*Proceedings of AAIM 2009 (Algorithmic Aspects
in Information and Management), San Francisco*

*Lecture Notes in Computer Science*, 5564:251--264, 2009.

Two graph isomorphism polytopes

*Discrete Mathematics*, 309:2934--2936, 2009.

Convex integer maximization via Graver bases

(with Jesus De Loera, Raymond Hemmecke,
Uriel Rothblum and Robert Weismantel),

*Journal of Pure and Applied Algebra*, 213:1569--1577, 2009.

Expressing combinatorial optimization problems by
systems of polynomial equations and the Nullstellensatz

(with Jesus De Loera, Jon Lee and Susan Margulies),
*Combinatorics, Probability and Computing*, 18:551--582, 2009.

Graphs of transportation polytopes

(with Jesus De Loera, Edward D. Kim and Francisco Santos),
*Journal of Combinatorial Theory Series A*, 116:1306--1325, 2009.

Convex discrete optimization

*Encyclopedia of Optimization*, 513--550, 2009.

N-fold integer programming
(also in
Virtual Special Issue -- 10 Year Anniversary of Discrete Optimization)

(with Jesus De Loera, Raymond Hemmecke and Robert Weismantel),
*Discrete Optimization*, 5:231--241, 2008.

Nonlinear matroid optimization and experimental design

(with Yael Berstein, Jon Lee, Hugo Maruri-Aguilar,
Eva Riccomagno, Robert Weismantel and Henry Wynn),

*SIAM Journal on Discrete Mathematics*, 22:901--919, 2008.

Nonlinear bipartite matching

(with
Yael Berstein),
*Discrete Optimization*, 5:53--65, 2008.

On test sets for nonlinear integer maximization

(with Jon Lee and Robert Weismantel),
*Operations Research Letters*, 36:439--443, 2008.

The convex dimension of a graph

(with
Nir Halman
and Uriel Rothblum).
*Discrete Applied Mathematics*, 155:1373--1383, 2007.

The use of edge-directions and
linear programming to enumerate vertices

(with Uriel Rothblum),
*Journal of Combinatorial Optimization*, 14:153--164, 2007.

Entry uniqueness in margined tables
(also
slides of talk at PSD in Rome)

*Proceedings of PSD 2006 - Eurostat Conference on
Privacy in Statistical Databases, Rome*

*Lecture Notes in Computer Science*, 4302:94--101, 2006.

All linear and integer programs are slim 3-way transportation programs

(with Jesus De Loera),
*SIAM Journal on Optimization*, 17:806--821, 2006.

Markov bases of three-way tables are arbitrarily complicated

(with Jesus De Loera),
*Journal of Symbolic Computation*, 41:173--181, 2006.

Permutohedra and minimal matrices

(with Ernesto Vallejo),
*Linear Algebra and its Applications*, 412:471--489, 2006.

Edge-directions of standard polyhedra
with applications to network flows

(with Uriel Rothblum and Yoav Tangir),
*Journal of Global Optimization*, 33:109--122, 2005.

All rational polytopes are transportation polytopes
and all polytopal integer sets are contingency tables
(also
slides of IPCO talk)

(with Jesus De Loera),
*Proceedings of IPCO 2004
(MPS Symposium on Integer Programming and Combinatorial Optimization), NYC*

*Lecture Notes in Computer Science*, 3064:338--351, 2004.

Nowhere-zero flow polynomials
(also
slides of talk in
Paris)

*Journal of Combinatorial Theory Series A*, 108:205--215, 2004.

A note on the minimum number of edge-directions of a convex polytope

(with Rom Pinchasi),
*Journal of Combinatorial Theory Series A*, 107:147--151, 2004.

Convex combinatorial optimization
(also
slides
of talk at the Caesarea Rothschild Institute)

(with Uriel Rothblum),
*Discrete and Computational Geometry*, 32:549--566, 2004.

The complexity of three-way statistical tables

(with
Jesus De Loera),
*SIAM Journal on Computing*, 33:819--836, 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
(also
slides of talk at Oberwolfach)

(with Eric Babson and
Rekha Thomas),
*Advances in Applied Mathematics*, 30:529--544, 2003.

An adaptive algorithm for vector partitioning

(with
Komei Fukuda
and Vera Rosta),
*Journal of Global Optimization*, 25:305--319, 2003.

Social network coordination and graph routing

(with Elisheva Sperber),
*Networks, 41:44--50, 2003.
*

*
Automated transformations for PDE systems with
applications to multigrid solvers
(with Yossi Gil, Zvika Gutterman and Irad Yavneh),
SIAM Journal on Scientific Computing, 24:886--904, 2002.
*

*
Momentopes, the complexity of vector partitioning,
and Davenport Schinzel sequences
(with Sharon Aviran),
Discrete and Computational Geometry, 27:409--417, 2002.
*

*
Solitaire lattices
(with
Antoine Deza),
Graphs and Combinatorics, 18:227--243, 2002.
*

*
Vertex characterization of partition polytopes
of bipartitions and of planar point sets
(with Sharon Aviran, Nisan Lev-Tov and Uriel 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 objectice functions
(with Leonard Schulman),
Mathematics of Operations Research, 26:583--590, 2001.
*

*
Linear shaped partition problems
(with Frank Hwang and Uriel Rothblum),
Operations Research Letters, 26:159--163, 2000.
*

*
*

*
Explicit solution of partitioning problems
over a 1-dimensional parameter space
(with Frank Hwang and Uriel Rothblum),
Naval Research Logistics, 47:531--540, 2000.
*

*
*

*
A combinatorial approach to the solitaire game
(with David Avis and Antoine Deza),
IEICE Transactions on Fundamentals of Electronics,
Communications and Computer Sciences, E83-A:656-661, 2000.
*

*
A polynomial time algorithm for shaped partition problems
(with Frank Hwang and Uriel Rothblum),
SIAM Journal on Optimization, 10:70--81, 1999.
*

*Cutting corners
(with
Bernd Sturmfels),
Advances in Applied Mathematics, 23:29--48, 1999.
*

*Separable partitions
(or reprint format through DAM's Editors' Choice, 1999 Edition)
(also
related info)
(with
Noga Alon),
Discrete Applied Mathematics, 91:39--51, 1999.
*

*
Representations and characterizations of vertices of bounded-shape
partition polytopes
(with Frank Hwang and Uriel Rothblum),
Linear Algebra and its Applications, 278:263--284, 1998.
*

*
Strongly signable and partitionable posets
European Journal of Combinatorics, 18:921--938, 1997.
*

*
Colourful linear programming and its relatives
(with
Imre Barany),
Mathematics of Operations Research, 22:550--567, 1997.
*

*
Caratheodory's theorem: colourful and applicable,
(with Imre Barany),
Bolyai Society Mathematical Studies, 6:11--21, 1997,
*

*
Determination of social laws for multi-agent mobilization
(with Moshe Tennenholtz),
Artificial Intelligence, 95:155--167, 1997.
*

*
A colorful determinantal identity, a conjecture of Rota,
and Latin squares
The American Mathematical Monthly, 104:156--159, 1997.
*

*
Signable posets and partitionable simplicial complexes
(with Peter Kleinschmidt),
Discrete and Computational Geometry, 15:443--466, 1996.
*

*
Lattice-free polytopes and their diameter
(with Michel Deza),
Discrete and Computational Geometry, 13:59--75, 1995.
*

*
A quantitative Steinitz theorem
(with Bernd Sturmfels),
Beiträge 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 Bernd 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 Peter 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.
*