Theory of linear and integer programming
Theory of linear and integer programming
An oracle-polynomial time augmentation algorithm for integer programming
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Higher Lawrence configurations
Journal of Combinatorial Theory Series A
A finiteness theorem for Markov bases of hierarchical models
Journal of Combinatorial Theory Series A
Dynamic-Programming Approximations for Stochastic Time-Staged Integer Multicommodity-Flow Problems
INFORMS Journal on Computing
Finiteness Theorems in Stochastic Integer Programming
Foundations of Computational Mathematics
New Formulations for Optimization under Stochastic Dominance Constraints
SIAM Journal on Optimization
A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse
Mathematical Programming: Series A and B
A polynomial oracle-time algorithm for convex integer minimization
Mathematical Programming: Series A and B
Discrete Optimization
Optimality criterion for a class of nonlinear integer programs
Operations Research Letters
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In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochastic integer programs with second-order dominance constraints and stochastic integer multi-commodity flows, which (for fixed blocks) can be solved in polynomial time in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions.