 
Summary: Revisiting the COUNTER Algorithms for List Update
Susanne Albers Michael Mitzenmachery
Abstract
COUNTER algorithms, a familyof randomized algorithms for the list update problem, were
introduced by Reingold, Westbrook, and Sleator 7]. They showed that for any > 0, there
exist COUNTER algorithms that achieve a competitive ratio of
p
3 + . In this paper we
use a mixture of two COUNTER algorithms to achieve a competitiveness of 12=7, which is
less than
p3. Furthermore, we demonstrate that it is impossible to prove a competitive ratio
smallerthan 12=7 for any mixture of COUNTER algorithmsusing the type of potential function
argument that has been used so far. We also provide new lower bounds for the competitiveness
of COUNTER algorithms in the standard cost model, including a 1.625 lower bound for the
variant BIT and a matching 12/7 lower bound for our algorithm.
Keywords: List update; Online algorithms; Randomized algorithms; Data structures.
1 Introduction
The list update problem, a fundamental and extensively studied online problem, is to maintain an
unsorted linear linked list so as to minimize the total cost of accesses on a sequence of requests. (The
formal de nition of the problem is given in the next section.) List update algorithms are useful
