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
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
Improved Randomized On-Line Algorithms for the List Update Problem
SIAM Journal on Computing
Online computation and competitive analysis
Online computation and competitive analysis
A new lower bound for the list update problem in the partial cost model
Theoretical Computer Science
Optimal Projective Algorithms for the List Update Problem
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
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
List factoring and relative worst order analysis
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Parameterized analysis of paging and list update algorithms
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Online and offline access to short lists
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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The list update problem is a classical online problem, with an optimal competitive ratio that is still open, known to be 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 the TIMESTAMP algorithm TS. This and almost all other list update algorithms, like MTF, are projective in the sense that they can be defined by looking only at any pair of list items at a time. Projectivity (also known as “list factoring”) 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 article, we characterize all projective list update algorithms and show that their competitive ratio is never smaller than 1.6 in the partial cost model. Therefore, COMB is a best possible projective algorithm in this model.