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The Joint Replenishment Problem (JRP) deals with optimizing shipments of goods from a supplier to retailers through a shared warehouse. Each shipment involves transporting goods from the supplier to the warehouse, at a fixed cost C, followed by a redistribution of these goods from the warehouse to the retailers that ordered them, where transporting goods to… (More)

- Christoph Dürr, Lukasz Jez, Nguyen Kim Thang
- J. Scheduling
- 2009

We consider an online scheduling problem, motivated by the following online auction setting. A non-storable perishable good is produced at a regular rate. It has to be sold immediately to customers whose offers arrive on-line. More formally, we consider the online scheduling problem with preemptions, where each job j is revealed at release time rj , has… (More)

- Marcin Bienkowski, Martin Böhm, +7 authors Pavel Veselý
- ESA
- 2016

In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edgeweighted tree T , and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also… (More)

- Nikhil Bansal, Marek Eliáš, Lukasz Jez, Grigorios Koumoutsos
- SODA
- 2017

We study the k-server problem in the resource augmentation setting i.e., when the performance of the online algorithm with k servers is compared to the offline optimal solution with h ≤ k servers. The problem is very poorly understood beyond uniform metrics. For this special case, the classic kserver algorithms are roughly (1 + 1/ )-competitive when k = (1… (More)

- Pawel Gawrychowski, Artur Jez, Lukasz Jez
- Theory of Computing Systems
- 2010

Let $\pi'_{w}$ denote the failure function of the Knuth-Morris-Pratt algorithm for a word w. In this paper we study the following problem: given an integer array $A'[1 \mathinner {\ldotp \ldotp }n]$ , is there a word w over an arbitrary alphabet Σ such that $A'[i]=\pi'_{w}[i]$ for all i? Moreover, what is the minimum cardinality of Σ required? We give an… (More)

- Marcin Bienkowski, Marek Chrobak, Lukasz Jez
- WAOA
- 2008

In the buffer management problem with bounded delay, weighted packets arrive at a network switch over time, and the goal is to send those packets before their deadlines while maximizing the total weight of the packets sent. In the 2-bounded delay case, each packet has to be sent either in the step of its release or in the next step. In the deterministic… (More)

- Marcin Bienkowski, Marek Chrobak, +4 authors Grzegorz Stachowiak
- Algorithmica
- 2009

We consider online competitive algorithms for the problem of collecting weighted items from a dynamic queue S. The content of S varies over time. An update to S can occur between any two consecutive time steps, and it consists in deleting any number of items at the front of S and inserting other items into arbitrary locations in S. At each time step we are… (More)

- Lukasz Jez, Fei Li, Jay Sethuraman, Clifford Stein
- ACM Trans. Algorithms
- 2012

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… (More)

- Ilan Reuven Cohen, Alon Eden, Amos Fiat, Lukasz Jez
- SODA
- 2015

We consider dynamic pricing schemes in online settings where selfish agents generate online events. Previous work on online mechanisms has dealt almost entirely with the goal of maximizing social welfare or revenue in an auction settings. This paper deals with quite general settings and minimizing social costs. We show that appropriately computed posted… (More)

- Lukasz Jez
- ArXiv
- 2009

We study the Buffer Management with Bounded Delay problem, introduced by Kesselman et al. [4], or, in the standard scheduling terminology, the problem of online scheduling of unit jobs to maximise weighted throughput. The adaptive-online adversary model for this problem has recently been studied by Bieńkowski et al. [2], who proved a lower bound of 4 3 on… (More)