Poly-logarithmic adaptive algorithms require unconditional primitives

This paper studies the step complexity of adaptive algorithms using primitives stronger than reads and writes. We first consider unconditional primitives, like fetch&inc, which modify the value of the register to which they are applied, regardless of its current value. Unconditional primitives admit snapshot algorithms with O(log k) step complexity, where k is the total or the point contention. These algorithms combine a renaming algorithm with a mechanism for propagating values so they can be quickly collected. When only conditional primitives, e.g., compare&swap or LL/SC, are used (in addition to reads and writes), we show that any collect algorithm must perform Ω(k) steps, in an execution with total contention k ∈ O(log log n). The lower bound applies for snapshot and renaming, both one-shot and long-lived. Note that there are snapshot algorithms whose step complexity is polylogarithmic in n using only reads and writes, but there are no adaptive algorithms whose step complexity is polylogarithmic in the contention, even when compare&swap and LL/SC are used.