Combining Initial Segments of Lists

  • Manfred K. Warmuth
  • Wouter M. Koolen
  • David P. Helmbold
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6925)


We propose a new way to build a combined list from K base lists, each containing N items. A combined list consists of top segments of various sizes from each base list so that the total size of all top segments equals N. A sequence of item requests is processed and the goal is to minimize the total number of misses. That is, we seek to build a combined list that contains all the frequently requested items. We first consider the special case of disjoint base lists. There, we design an efficient algorithm that computes the best combined list for a given sequence of requests. In addition, we develop a randomized online algorithm whose expected number of misses is close to that of the best combined list chosen in hindsight. We prove lower bounds that show that the expected number of misses of our randomized algorithm is close to the optimum. In the presence of duplicate items, we show that computing the best combined list is NP-hard. We show that our algorithms still apply to a linearized notion of loss in this case. We expect that this new way of aggregating lists will find many ranking applications.


Initial Segment Online Algorithm Deterministic Algorithm Probabilistic Algorithm Cache Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Manfred K. Warmuth
    • 1
  • Wouter M. Koolen
    • 2
    • 3
  • David P. Helmbold
    • 1
  1. 1.Department of Computer ScienceUC Santa CruzUSA
  2. 2.Department of Computer ScienceRoyal Holloway, University of LondonUK
  3. 3.Centrum Wiskunde en InformaticaAmsterdam

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