Contention-free complexity of shared memory algorithms

While the worst-case time complexity measures the maximum time needed to solve a problem over all runs, the contention-free time complexity indicates the maximum time needed when a process executes by itself without competition from other processes. Since contention should be rare in well-designed systems, it is important to design algorithms which perform well also in the absence of contention. We study the contention-free time complexity of shared memory algorithms using two measures: step complexity that counts the number of accesses to shared registers, and register complexity that measures the number of different registers accessed. Depending on the architecture, one of the two measures more accurately reflects the time taken. We provide lower and upper bounds for the contentionfree step and register complexity of solving the mutual exclusion problem as a function of the number of processes and the size of the biggest register that can be accessed in one atomic step. We also present bounds on the worst-case and contention-free step and register complexities of solving the naming problem. These bounds illustrate how the proposed definitions are useful in differentiating among the computational powers of different primitives.