Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minmax regret solutions for minimax optimization problems with uncertainty
Operations Research Letters
An approximation algorithm for interval data minmax regret combinatorial optimization problems
Information Processing Letters
A Branch and Bound algorithm for the minimax regret spanning arborescence
Journal of Global Optimization
The minimum spanning tree problem with fuzzy costs
Fuzzy Optimization and Decision Making
Choosing robust solutions in discrete optimization problems with fuzzy costs
Fuzzy Sets and Systems
On the approximability of minmax (regret) network optimization problems
Information Processing Letters
An approximation algorithm for interval data minmax regret combinatorial optimization problems
Information Processing Letters
The minimum risk spanning tree problem
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Some tractable instances of interval data minmax regret problems: bounded distance from triviality
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Heuristics for the central tree problem
Journal of Heuristics
Criticality analysis of activity networks under interval uncertainty
Journal of Scheduling
Exact and heuristic algorithms for the interval data robust assignment problem
Computers and Operations Research
Deterministic risk control for cost-effective network connections
Theoretical Computer Science
Reduction approaches for robust shortest path problems
Computers and Operations Research
Possibilistic bottleneck combinatorial optimization problems with ill-known weights
International Journal of Approximate Reasoning
Complexity of the min-max (regret) versions of cut problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Some tractable instances of interval data minmax regret problems
Operations Research Letters
Operations Research Letters
The robust shortest path problem in series-parallel multidigraphs with interval data
Operations Research Letters
Minmax regret bottleneck problems with solution-induced interval uncertainty structure
Discrete Optimization
Complexity of the min-max (regret) versions of min cut problems
Discrete Optimization
Complexity of the min-max and min-max regret assignment problems
Operations Research Letters
Robust shortest path problem based on a confidence interval in fuzzy bicriteria decision making
Information Sciences: an International Journal
On exact solutions for the Minmax Regret Spanning Tree problem
Computers and Operations Research
Hi-index | 0.05 |
We consider the minimum spanning tree and the shortest path problems on a network with uncertain lengths of edges. In particular, for any edge of the network, only an interval estimate of the length of the edge is known, and it is assumed that the length of each edge can take on any value from the corresponding interval of uncertainty, regardless of the values taken by the lengths of other edges. It is required to find a minmax regret solution. We prove that both problems are NP-hard even if the bounds of all intervals of uncertainty belong to {0,1}. The interval data minmax regret shortest path problem is NP-hard even if the network is directed, acyclic, and has a layered structure. We show that the problems are polynomially solvable in the practically important case where the number of edges with uncertain lengths is fixed or is bounded by the logarithm of a polynomial function of the total number of edges. We discuss implications of these results for the general theory of interval data minmax regret combinatorial optimization.