Offline List Update is NP-Hard

  • Authors:
  • Christoph Ambühl

  • Affiliations:
  • -

  • Venue:
  • ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
  • Year:
  • 2000

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Abstract

In the offline list update problem, we maintain an unsorted linear list used as a dictionary. Accessing the item at position i in the list costs i units. In order to reduce access cost, we are allowed to update the list at any time by transposing consecutive items at a cost of one unit. Given a sequence σ of requests one has to serve in turn, we are interested in the minimal cost needed to serve all requests. Little is known about this problem. The best algorithm so far needs exponential time in the number of items in the list. We show that there is no polynomial algorithm unless P = NP.