Single machine flow-time scheduling with a single breakdown
Acta Informatica
Annals of Operations Research
Single machine flow-time scheduling with scheduled maintenance
Acta Informatica
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Online Weighted Flow Time and Deadline Scheduling
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Universal approximations for TSP, Steiner tree, and set cover
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximation schemes for a class of subset selection problems
Theoretical Computer Science
Computers and Industrial Engineering
Incremental Medians via Online Bidding
Algorithmica
Approximating Single Machine Scheduling with Scenarios
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
A Survey on Approximation Algorithms for Scheduling with Machine Unavailability
Algorithmics of Large and Complex Networks
Survey on Oblivious Routing Strategies
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
A primal-dual approximation algorithm for min-sum single-machine scheduling problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the performance of smith's rule in single-machine scheduling with nonlinear cost
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. For the objective of minimizing the total weighted completion time, we design a polynomial time deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the disruptions in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. As a direct consequence of our results, we answer affirmatively the question of whether a constant approximation algorithm exists for the offline version of the problem when machine unavailability periods are known in advance. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(logn/ loglogn) worse than an optimal sequence. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a non-trivial algorithm with a small constant performance guarantee.