TY - GEN

T1 - Universal sequencing on a single machine

AU - Epstein, Leah

AU - Levin, Asaf

AU - Marchetti-Spaccamela, Alberto

AU - Megow, Nicole

AU - Mestre, Julián

AU - Skutella, Martin

AU - Stougie, Leen

PY - 2010

Y1 - 2010

N2 - 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(log n/ log log n) 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.

AB - 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(log n/ log log n) 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.

UR - http://www.scopus.com/inward/record.url?scp=77954414894&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-13036-6_18

DO - 10.1007/978-3-642-13036-6_18

M3 - Conference contribution

AN - SCOPUS:77954414894

SN - 3642130356

SN - 9783642130359

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 230

EP - 243

BT - Integer Programming and Combinatorial Optimization - 14th International Conference, IPCO 2010, Proceedings

T2 - 14th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2010

Y2 - 9 June 2010 through 11 June 2010

ER -