Approximation algorithms for NP-hard problems
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine
Discrete Applied Mathematics
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On the Power of Unique 2-Prover 1-Round Games
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Robust Combinatorial Optimization with Exponential Scenarios
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Approximating min-max (regret) versions of some polynomial problems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Operations Research Letters
On the approximability of robust spanning tree problems
Theoretical Computer Science
Universal sequencing on a single machine
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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In the field of robust optimization, the goal is to provide solutions to combinatorial problems that hedge against variations of the numerical parameters. This constitutes an effort to design algorithms that are applicable in the presence of uncertainty in the definition of the instance. We study the single machine scheduling problem with the objective to minimize the weighted sum of completion times. We model uncertainty by replacing the vector of numerical values in the description of the instance by a set of possible vectors, called scenarios. The goal is to find the schedule with minimum value in the worst-case scenario.We first show that the general problem is intractable by proving that it cannot be approximated within O(log1 茂戮驴 茂戮驴n) for any 茂戮驴 0, unless NP has quasi-polynomial algorithms. We then study more tractable special cases and obtain an LP based 2-approximation algorithm for the unweighted case. We show that our analysis is tight by providing a matching lower bound on the integrality gap of the LP. Moreover, we prove that the unweighted version is NP-hard to approximate within a factor less than 6/5. We conclude by presenting a polynomial time algorithm based on dynamic programming for the case when the number of scenarios and the values of the instance are bounded by some constant.