On list update and work function algorithms

Authors:
Eric J. Anderson;Kirsten Hildrum;Anna R. Karlin;April Rasala;Michael Saks
Affiliations:
Department of Computer Science and Engineering, University of Washington, Box 352350, Seattle, WA;Computer Science Division, University of California, Berkeley;Department of Computer Science and Engineering, University of Washington, Box 352350, Seattle, WA;Laboratory of Computer Science, Massachusetts Institute of Technology;Department of Mathematics, Rutgers University
Venue:
Theoretical Computer Science
Year:
2002

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Abstract

The list update problem, a well-studied problem in dynamic data structures, can be described abstractly as a metrical task system. In this paper, we prove that a generic metrical task system algorithm, called the work function algorithm, has constant competitive ratio for list update. In the process, we present a new formulation of the well-known "list factoring" technique in terms of a partial order on the elements of the list. This approach leads to a new simple proof that a large class of online algorithms, including Move-To-Front, is (2 - 1/k)-competitive, for k the list length.