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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)
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)
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)
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)
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)
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)
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)
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)