Preemptive Scheduling of Equal-Length Jobs to Maximize Weighted Throughput

We study the problem of computing a preemptive schedule of equal-length jobs with given release times, deadlines and weights. Our goal is to maximize the weighted throughput, which is the total weight of completed jobs. In Graham's notation this problem is described as (1 | r_j;p_j=p;pmtn | sum w_j U_j). We provide an O(n^4)-time algorithm for this problem, improving the previous bound of O(n^{10}) by Baptiste.Comment: gained one author and lost one degree in the complexit

Preemptive Online Scheduling: Optimal Algorithms for All Speeds

Our main result is an optimal online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize makespan. The algorithm is deterministic, yet it is optimal even among all randomized algorithms. In addition, it is optimal for any fixed combination of speeds of the machines, and thus our results subsume all the previous work on various special cases. Together with a new lower bound it follows that the overall competitive ratio of this optimal algorithm is between 2.054 and e ≈ 2.718.

Improved Online Algorithms for Buffer Management in QoS Switches

We consider the following buffer management problem arising in QoS networks: packets with specified weights and deadlines arrive at a network switch and need to be forwarded so that the total weight of forwarded packets is maximized. Packets not forwarded before their deadlines are lost. The main result of the paper is an online 64/33 ≈ 1.939-competitive algorithm – the first deterministic algorithm for this problem with competitive ratio below 2. For the 2-uniform case we give an algorithm with ratio ≈ 1.377 and a matching lower bound.

Online Scheduling of Equal-Length Jobs: Randomization and Restarts Help

We consider the following scheduling problem. The input is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a single-processor, non-preemptive schedule of these jobs that maximizes the number of completed jobs. In the online version, each job arrives at its release time. We give two online algorithms with competitive ratios below 2 and show several lower bounds on the competitive ratios. First, we give a -competitive randomized algorithm. Our algorithm needs only one fair random bit, as it chooses one of two (nearly identical) deterministic algorithms, each with probability . We also show a lower bound of for barely random algorithms, that (with arbitrary probability) choose one of two deterministic algorithms. Next, we give a deterministic -competitive algorithm in the model that allows restarts, and we show that in this model the ratio is optimal. For randomized algorithms with restarts we show a lower bound of