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

Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania

Collections: Computer Technologies and Information Sciences