Approximation of min-max and min-max regret versions of some combinatorial optimization problems

@article{Aissi2007ApproximationOM,
  title={Approximation of min-max and min-max regret versions of some combinatorial optimization problems},
  author={Hassene Aissi and Cristina Bazgan and Daniel Vanderpooten},
  journal={Eur. J. Oper. Res.},
  year={2007},
  volume={179},
  pages={281-290}
}

Figures and Tables from this paper

Min-max and min-max regret versions of combinatorial optimization problems: A survey
On scenario aggregation to approximate robust combinatorial optimization problems
TLDR
This paper presents a simple extension of the midpoint method based on scenario aggregation, which improves the current best K-approximation result to an $$(\varepsilon K)$$(εK)-approximating for any desired $$\varpsilon > 0$$ε>0.
On Scenario Aggregation to Approximate Robust Optimization Problems
TLDR
This paper presents a simple extension of the midpoint method based on scenario aggregation, which improves the current best K-approximation result to an (eK)-approximating for any desired e>0.
Randomized Minmax Regret for Combinatorial Optimization Under Uncertainty
TLDR
A randomized model where the optimizing player selects a probability distribution (corresponding to a mixed strategy) over solutions and the adversary selects costs with knowledge of the player’s distribution, but not its realization is considered, and it is proved that minmax regret problems are NP-hard under general convex uncertainty.
The interval min–max regret knapsack packing-delivery problem
ABSTRACT This paper studies an interval data min–max regret (IDMR) version of the packing-delivery problem, in which a 0-1 knapsack problem is for parcel packing and a capacitated travelling salesman
Combinatorial Optimization Problems with Balanced Regret
TLDR
It is shown that, while the classic regret setting with budgeted uncertainty sets can be solved in polynomial time, the balanced regret problem becomes NP-hard.
Minmax regret combinatorial optimization problems: an Algorithmic Perspective
TLDR
The computational complexity of some classic combinatorial optimization problems using MMR approach is discussed, the design of several algorithms for these problems are analyzed, and the study of some specific research problems in this attractive area is suggested.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 17 REFERENCES
Fast approximation schemes for multi-criteria combinatorial optimization
  • H. Safer
  • Mathematics, Computer Science
  • 1992
TLDR
In this paper, necessary and sufficient conditions are developed for the existence of such a fast approximation scheme for a problem and an appropriate form of problem reduction is introduced to facilitate the application of these conditions to a variety of problems.
Approximating Multiobjective Knapsack Problems
TLDR
The first known polynomial-time approximation scheme (PTAS), based on linear programming, is presented and is based on a new approach to the single-objective knapsack problem using a partition of the profit space into intervals of exponentially increasing length.
Approximation Algorithms for NP-Hard Problems
TLDR
This book reviews the design techniques for approximation algorithms and the developments in this area since its inception about three decades ago and the "closeness" to optimum that is achievable in polynomial time.
On the approximability of trade-offs and optimal access of Web sources
TLDR
These concepts and techniques are applied to formulate and solve approximately a cost-time-quality trade-off for optimizing access to the World-Wide Web, in a model first studied by Etzioni et al. (1996).
General Techniques for Combinatorial Approximation
TLDR
This is a tutorial on general techniques for combinatorial approximation, which generate fully polynomial time approximation schemes for a large number of NP-complete problems.
Robust Discrete Optimization and its Applications
TLDR
This paper presents four approaches to handle Uncertainty in Decision Making using a Robust Discrete Optimization Framework and results show how these approaches can be applied to real-world problems.
Computers and Intractability: A Guide to the Theory of NP-Completeness
Horn formulae play a prominent role in artificial intelligence and logic programming. In this paper we investigate the problem of optimal compression of propositional Horn production rule knowledge
...
1
2
...