 
Summary: Adaptive algorithms utilyzing adaptive collect
and snapshot
Yehuda Afek \Lambda Eli Gafni y Michael Merritt z
August 25, 1999
Abstract
Several adaptive algorithms are automatically generated via a simple transformation from
singlewriter multireader algorithms, using the O(k) adaptive collect algorithm of Attiya and
Fouren [AF98a]. Among these algorithms are an adaptive snapshot algorithm with step complex
ity O(k 2 ), and three algorithms solving (2k \Gamma 1)renaming, but with high step complexities (k4 k ,
\Omega\Gamma/ k=2 ), and k 3 ), where k is the contention, the number of processes actually taking steps during
the run of the algorithm. The transformation does not always produce an adaptive algorithm:
the O(n log n) latticeagreement (one shot snapshot) algorithm of Attiya and Rachman [AR93]
is one example. However, we show that a simple modification of the original algorithm allows
the transformation to produce an adaptive, O(k log k) latticeagreement algorithm, matching the
bestknown step complexity of Attiya and Fouren's algorithm [AF98].
Finally, we present a speciallytailored algorithm for (2k \Gamma 1)renaming that uses any of these
adaptive latticeagreement or snapshot algorithms as a component. Building on a renaming
algorithm of Attiya and Fouren, the adaptive (2k \Gamma 1)renaming algorithm has step complexity
O(k 2 ), which is better than any other known adaptive algorithm for optimal renaming.
1 Introduction
