A φ-competitive algorithm for collecting items with increasing weights from a dynamic queue

  • Authors:

  • Marcin Bienkowski;Marek Chrobak;Christoph Dürr;Mathilde Hurand;Artur Je;Ukasz Je;Grzegorz Stachowiak

  • Affiliations:

  • Institute of Computer Science, University of Wrocaw, 50-383 Wrocaw, Poland;Department of Computer Science, University of California, Riverside, CA 92521, United States;CNRS, LIP6, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France;Google, 8002 Zürich, Switzerland;Institute of Computer Science, University of Wrocaw, 50-383 Wrocaw, Poland;Institute of Computer Science, University of Wrocaw, 50-383 Wrocaw, Poland and Institute of Mathematics, Academy of Sciences of the Czech Republic, itná 25, 115 67 Praha 1, Czech Republic;Institute of Computer Science, University of Wrocaw, 50-383 Wrocaw, Poland

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

The bounded-delay packet scheduling (or buffer management) problem is to schedule transmissions of packets arriving in a buffer of a network link. Each packet has a deadline and a weight associated with it. The objective is to maximize the weight of packets that are transmitted before their deadlines, assuming that only one packet can be transmitted in one time step. Online packet scheduling algorithms have been extensively studied. It is known that no online algorithm can achieve a competitive ratio better than @f~1.618 (the golden ratio), while the currently best upper bound on the competitive ratio is 22-1~1.824. Closing the gap between these bounds remains a major open problem. The above mentioned lower bound of @f uses instances where item weights increase exponentially over time. In fact, all lower bounds for various versions of buffer management problems involve instances of this type. In this paper, we design an online algorithm for packet scheduling with competitive ratio @f when packet weights are increasing, thus matching this lower bound. Our algorithm applies, in fact, to a much more general version of packet scheduling, where only the relative order of the deadlines is known, not their exact values.