Amortized efficiency of list update and paging rules
Communications of the ACM
Amortized analyses of self-organizing sequential search heuristics
Communications of the ACM - Lecture notes in computer science Vol. 174
An optimal online algorithm for metrical task systems
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
On the power of randomization in online algorithms
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Two results on the list update problem
Information Processing Letters
A lower bound for randomized list update algorithms
Information Processing Letters
A combined BIT and TIMESTAMP algorithm for the list update problem
Information Processing Letters
Online computation and competitive analysis
Online computation and competitive analysis
Improved randomized on-line algorithms for the list update problem
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
A new lower bound for the list update problem in the partial cost model
Theoretical Computer Science
Self-Organizing Data Structures
Developments from a June 1996 seminar on Online algorithms: the state of the art
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Offline List Update is NP-Hard
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Optimal lower bounds for projective list update algorithms
ACM Transactions on Algorithms (TALG)
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The list update problem is a classical online problem, with an optimal competitive ratio that is still open, somewhere between 1.5 and 1.6. An algorithm with competitive ratio 1.6, the smallest known to date, is COMB, a randomized combination of BIT and TIMESTAMP. This and many other known algorithms, like MTF, are projective in the sense that they can be defined by only looking at any pair of list items at a time. Projectivity simplifies both the description of the algorithm and its analysis, and so far seems to be the only way to define a good online algorithm for lists of arbitrary length. In this paper we characterize all projective list update algorithms and show their competitive ratio is never smaller than 1.6. Therefore, COMB is a best possible projective algorithm, and any better algorithm, if it exists, would need a non-projective approach.