Collecting weighted items from a dynamic queue

  • Authors:

  • Marcin Bienkowski;Marek Chrobak;Christoph Dürr;Mathilde Hurand;Artur Jeż;Lukasz Jeż;Grzegorz Stachowiak

  • Affiliations:

  • University of Wroclaw, Wroclaw, Poland;University of California, Riverside, CA;CNRS, LIX UMR, Palaiseau, France;Google, Zürich, Switzerland;University of Wroclaw, Wroclaw, Poland;University of Wroclaw, Wroclaw, Poland;University of Wroclaw, Wroclaw, Poland

  • Venue:
  • SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
  • Year:
  • 2009

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Abstract

We consider the problem of collecting weighted items from a dynamic queue S. Before each step, some items at the front of S can be deleted and some other items can be added to S at any place. An item, once deleted, cannot be re-inserted --- in other words, it "expires". We are allowed to collect one item from S per step. Each item can be collected only once. The objective is to maximize the total weight of the collected items. We study the online version of the dynamic queue problem. It is quite easy to see that the greedy algorithm that always collects the maximum-value item is 2-competitive, and that no deterministic online algorithm can be better than 1.618-competitive. We improve both bounds: We give a 1.89-competitive algorithm for general dynamic queues and we show a lower bound of 1.632 on the competitive ratio. We also provide other upper and lower bounds for restricted versions of this problem. The dynamic queue problem is a generalization of the well-studied buffer management problem, and it is an abstraction of the buffer management problem for network links with intermittent access.