Universal sequencing on an unreliable machine

Leah Epstein, Asaf Levin, Alberto Marchetti-Spaccamela, Nicole Megow, Julian Mestre, Martin Skutella, Leen Stougie

Research output: Contribution to journalArticlepeer-review


We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. Our objective is to minimize ?wjf(Cj) for any nondecreasing, nonnegative, differentiable cost function f(Cj ). We aim for a universal solution that performs well without adaptation for all cost functions for any possible machine behavior. We design a 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 machine behavior in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both performance guarantees are best possible for any unbounded cost function. Our algorithms can be adapted to run in polynomial time with slightly increased cost. 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 O(log n/ log log n) worse than an optimal sequence for any unbounded cost function. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a nontrivial algorithm with a small constant performance guarantee.

Original languageEnglish
Pages (from-to)565-586
Number of pages22
JournalSIAM Journal on Computing
Issue number3
StatePublished - 2012


  • Machine speed
  • Min-sum objective
  • Scheduling
  • Single machine
  • Universal solution
  • Unreliable machine
  • Worst case guarantee

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


Dive into the research topics of 'Universal sequencing on an unreliable machine'. Together they form a unique fingerprint.

Cite this