The source text discusses online job scheduling, where jobs arrive dynamically and the scheduler must make immediate decisions without knowing what jobs will come next. It compares online algorithms with an optimal algorithm that knows all jobs in advance, using competitive ratio as the measure of performance.
The text says standard non-preemptive algorithms fail in this setting, with competitive ratio approaching zero. It explains that a bad choice, such as scheduling one long job, can block many future smaller jobs. In this setup, each completed job has equal weight, regardless of length.
To address the online problem, the text studies two models that allow an active job to be interrupted if a better opportunity appears. Only jobs that are restarted and later completed non-preemptively count as successful.
Under Interruption with restarts, an online algorithm may interrupt a job. The partial work already done is lost, but the job remains in the system and can be tried again. The text says this flexibility is highly beneficial: a variant of Greedy that iteratively schedules the job that finishes earliest achieves a 1/2-competitive ratio, matching the offline setting.
Under Interruption without restarts, all work on the interrupted job is lost and the job is discarded forever. The text says any online algorithm can still be forced into poor decisions, and the competitive ratio of all online algorithms approaches zero.
From these hard cases, the text turns to a practical scenario where all jobs share a common deadline, such as data processing finishing by a nightly batch run. For common deadline instances, it says the authors devise novel constant competitive algorithms. In the simple setting of a unit capacity profile, where only a single job can be scheduled at any time, the algorithm keeps a tentative schedule by assigning arrived jobs to disjoint time intervals. When a new job arrives, the algorithm updates that schedule by taking the first applicable action from four possible actions.
Source: research.google.
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