Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Mathematics of Operations Research
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
Interval data minmax regret network optimization problems
Discrete Applied Mathematics
Mathematical Programming: Series A and B
Restricted Robust Uniform Matroid Maximization Under Interval Uncertainty
Mathematical Programming: Series A and B
Explicit Reformulations for Robust Optimization Problems with General Uncertainty Sets
SIAM Journal on Optimization
An approximation algorithm for interval data minmax regret combinatorial optimization problems
Information Processing Letters
Operations Research Letters
The robust shortest path problem in series-parallel multidigraphs with interval data
Operations Research Letters
Minmax regret solutions for minimax optimization problems with uncertainty
Operations Research Letters
On the complexity of the continuous unbounded knapsack problem with uncertain coefficients
Operations Research Letters
Complexity of the min-max and min-max regret assignment problems
Operations Research Letters
On the complexity of the robust spanning tree problem with interval data
Operations Research Letters
The robust spanning tree problem with interval data
Operations Research Letters
Scenario based robust line balancing: Computational complexity
Discrete Applied Mathematics
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We consider minmax regret bottleneck subset-type combinatorial optimization problems, where feasible solutions are some subsets of a finite ground set of cardinality n. The weights of elements of the ground set are uncertain; for each element, an uncertainty interval that contains its weight is given. In contrast with previously studied interval data minmax regret models, where the set of scenarios (possible realizations of the vector of weights) does not depend on the chosen feasible solution, we consider the problem with solution-induced interval uncertainty structure. That is, for each element of the ground set, a nominal weight from the corresponding uncertainty interval is fixed, and it is assumed that only the weights of the elements included in the chosen feasible solution can deviate from their respective nominal values. This uncertainty structure is motivated, for example, by network design problems, where the weight (construction cost, connection time, etc.) of an edge gets some ''real'' value, possibly different from its original nominal estimate, only for the edges (connections) that are actually implemented (built); or by capital budgeting problems with uncertain profits of projects, where only the profits of implemented projects can take ''real'' values different from the original nominal estimates. We present a polynomial O(n^2) algorithm for the problem on a uniform matroid of rank p, where feasible solutions are subsets of cardinality p of the ground set. For the special case where the minimum of the nominal weights is greater than the maximum of the lower-bound weights, we present a simple O(n+plogp) algorithm.