Contention-Free Complexity of Shared Memory Algorithms

Worst-case time complexity is a measure of the maximum time needed to solve a problem over all runs. Contention-free time complexity indicates the maximum time needed when a process executes by itself, without competition from other processes. Since contention is rare in well-designed systems, it is important to design algorithms which perform well in the absence of contention. We study the contention-free 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 contention-free step and register complexity 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 worst-case and contention-free step and register complexities of solving the naming problem. These bounds illustrate that the proposed complexity measures are useful in differentiating among the computational powers of different primitives.