Łukasz Jeż

Online scheduling of packets with agreeable deadlines

This article concerns an online packet scheduling problem that arises as a natural model for buffer management at a network router. Packets arrive at a router at integer time steps, and are buffered upon arrival. Packets have non-negative weights and integer deadlines that are (weakly) increasing in their arrival times. In each integer time step, at most one packet can be sent. The objective is to maximize the sum of the weights of the packets that are sent by their deadlines. The main results include an optimal (φ := (1 + √ 5)/2 ≈ 1.618)-competitive deterministic online algorithm, a (4/3 ≈ 1.33)-competitive randomized online algorithm against an oblivious adversary, and a 2-speed 1-competitive deterministic online algorithm. The analysis does not use a potential function explicitly, but instead modifies the adversarys buffer and credits the adversary to account for these modifications.

Online Scheduling of Jobs with Fixed Start Times on Related Machines

We consider online preemptive scheduling of jobs with fixed starting times revealed at those times on

Randomized Algorithms for Buffer Management with 2-Bounded Delay

m

Online Knapsack Revisited

m uniformly related machines, with the goal of maximizing the total weight of completed jobs. Every job has a size and a weight associated with it. A newly released job must be either assigned to start running immediately on a machine or otherwise it is dropped. It is also possible to drop an already scheduled job, but only completed jobs contribute their weights to the profit of the algorithm. In the most general setting, no algorithm has bounded competitive ratio, and we consider a number of standard variants. We give a full classification of the variants into cases which admit constant competitive ratio (weighted and unweighted unit jobs, and C-benevolent instances, which is a wide class of instances containing proportional-weight jobs), and cases which admit only a linear competitive ratio (unweighted jobs and D-benevolent instances). In particular, we give a lower bound of

The ( h, k )-server problem on bounded depth trees

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Scheduling multipacket frames with frame deadlines

m on the competitive ratio for scheduling unit weight jobs with varying sizes, which is tight. For unit size and weight we show that a natural greedy algorithm is