Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality
Mathematical Programming: Series A and B
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Mathematics of Operations Research
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Operations Research
Foreword: special issue on robust optimization
Mathematical Programming: Series A and B
Robust Combinatorial Optimization with Exponential Scenarios
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Two-Stage Robust Network Design with Exponential Scenarios
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Robust and Online Large-Scale Optimization
A robust approach to the chance-constrained knapsack problem
Operations Research Letters
Operations Research Letters
Robust solutions of uncertain linear programs
Operations Research Letters
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We consider robust counterparts of integer programs and combinatorial optimization problems (summarized as integer problems in the following), i.e., seek solutions that stay feasible if at most Γ-many parameters change within a given range. While there is an elaborate machinery for continuous robust optimization problems, results on robust integer problems are still rare and hardly general. We show several optimization and approximation results for the robust (with respect to cost, or few constraints) counterpart of an integer problem under the condition that one can optimize or approximate the original integer problem with respect to a piecewise linear objective (respectively piecewise linear constraints). For example, if there is a ρ-approximation for a minimization problem with non-negative costs and non-negative and bounded variables for piecewise linear objectives, then the cost robust counterpart can be ρ(1+ε)-approximated. We demonstrate the applicability of our approach on two classes of integer programs, namely, totally unimodular integer programs and integer programs with two variables per inequality. Further, for combinatorial optimization problems our method yields polynomial time approximations and pseudopolynomial, exact algorithms for Robust Unbounded Knapsack Problems.