List update problem

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The List Update or the List Access problem is a simple model used in the study of competitive analysis of online algorithms. Given a set of items in a list where the cost of accessing an item is proportional to its distance from the head of the list, e.g. a Linked List, and a request sequence of accesses, the problem is to come up with a strategy of reordering the list so that the total cost of accesses is minimized. The reordering can be done at any time but incurs a cost. The standard model includes two reordering actions:

  • A free transposition of the item being accessed anywhere ahead of its current position;
  • A paid transposition of a unit cost for exchanging any two adjacent items in the list. Performance of algorithms depend on the construction of request sequences by adversaries under various Adversary models

An online algorithm for this problem has to reorder the elements and serve requests based only on the knowledge of previously requested items and hence its strategy may not have the optimum cost as compared to an offline algorithm that gets to see the entire request sequence and devise a complete strategy before serving the first request.

Along with its original uses, this problem has been suggested to have a strong similarity to problems of improving global context and compressibility following a Burrows–Wheeler transform. Following this transform, files tend to have large regions with locally high frequencies, and compression efficiency is greatly improved by techniques that tend to move frequently-occurring characters toward zero, or the front of the "list". Due to this, methods and variants of Move-to-Front and frequency counts often follow the BWT algorithm to improve compressibility.