 
Summary: Contentionfree Complexity of Shared Memory Algorithms \Lambda
Rajeev Alur y Gadi Taubenfeld z
Abstract
Worstcase time complexity is a measure of the maximumtime needed to solve a problem
over all runs. Contentionfree time complexity indicates the maximum time needed
when a process executes by itself, without competition from other processes. Since
contention is rare in welldesigned systems, it is important to design algorithms which
perform well in the absence of contention. We study the contentionfree time complexity
of shared memory algorithms using two measures: step complexity, which counts the
number of accesses to shared registers; and register complexity, which measures the
number of different registers accessed. Depending on the system architecture, one of
the two measures more accurately reflects the elapsed time.
We provide lower and upper bounds for the contentionfree step and register com
plexity of solving the mutual exclusion problem as a function of the number of processes
and the size of the largest register that can be accessed in one atomic step. We also
present bounds on the worstcase and contentionfree step and register complexities
of solving the naming problem. These bounds illustrate that the proposed complex
ity measures are useful in differentiating among the computational powers of different
primitives.
\Lambda An abbreviated version of this paper appeared in the Proceedings of the 13th Annual ACM Symposium
