Lower bounds for on-line single-machine scheduling

The problem of scheduling jobs that arrive over time on a single machine is well-studied. We study the preemptive model and the model with restarts. We provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and unweighted total flow time. By using new techniques, we provide the first lower bounds for several of these problems, and we significantly improve the bounds that were known

Single machine batch scheduling with release times

Motivated by a high-throughput logging system, we investigate the single machine scheduling problem with batching, where jobs have release times and processing times, and batches require a setup time. Our objective is to minimize the total flow time, in the online setting. For the online problem where all jobs have identical processing times, we propose a 2-competitive algorithm and we prove acorresponding lower bound. Moreover, we show that if jobs with arbitrary processing times can be processed in any order, any online algorithm has a linear competitive ratio in the worst cas

Competitive Kill-and-Restart and Preemptive Strategies for Non-Clairvoyant Scheduling

We study kill-and-restart and preemptive strategies for the fundamental scheduling problem of minimizing the sum of weighted completion times on a single machine in the non-clairvoyant setting. First, we show a lower bound of~$3$ for any deterministic non-clairvoyant kill-and-restart strategy. Then, we give for any $b > 1$ a tight analysis for the natural $b$-scaling kill-and-restart strategy as well as for a randomized variant of it. In particular, we show a competitive ratio of $(1+3\sqrt{3})\approx 6.197$ for the deterministic and of $\approx 3.032$ for the randomized strategy, by making use of the largest eigenvalue of a Toeplitz matrix. In addition, we show that the preemptive Weighted Shortest Elapsed Time First (WSETF) rule is $2$-competitive when jobs are released online, matching the lower bound for the unit weight case with trivial release dates for any non-clairvoyant algorithm. Using this result as well as the competitiveness of round-robin for multiple machines, we prove performance guarantees smaller than $10$ for adaptions of the $b$-scaling strategy to online release dates and unweighted jobs on identical parallel machines.Comment: An extended abstract occurred in the Proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimizatio

Lower Bounds for on-Line Single-Machine Scheduling

The problem of scheduling jobs that arrive over time on a single machine is well-studied. We study the preemptive model and the model with restarts. We provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and unweighted total flow time. By using new techniques, we provide the first lower bounds for several of these problems, and we significantly improve the bounds that were known