发表机构
University of Calgary（卡尔加里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种保留历史独立性的高效随机化LL/SC实现，空间复杂度优于同类确定性算法，可支持STOC 2025提出的QHI动态哈希算法在硬件上的高效实现。
AI 中文摘要
我们研究在由n个进程组成的系统中，使用硬件中常用的有界基对象（CAS和寄存器）实现m个线性化LL/SC对象的基本问题，要求其具有恒定的期望步复杂度。假设每个进程最多有τ个未完成的LL操作，目前已知的最优确定性算法需要Ω(n²τ + m)个基对象（CAS和寄存器）[Blelloch和Wei，DISC 2020]。此前，尚未有可比的随机化算法被提出。通过采用随机化方法以及FADD（加法操作），结合CAS和寄存器，我们针对弱自适应对手得到了O(nτ + m)的空间复杂度上界。当m=O(1)时，该上界与使用CAS和寄存器的算法的下界相匹配[Aghazadeh和Woelfel，PODC 2015]。此外，我们提出的对象可被用于静止历史独立（QHI）算法：当对象上无操作待处理且无进程有未完成的LL操作时，其内部内存状态由m个LL/SC对象的值唯一确定。一个重要应用是STOC 2025上提出的QHI动态哈希算法，该算法使用Θ(m)个硬件LL/SC对象维护大小为m的哈希表[Attiya、Bender、Farach-Colton、Oshman和Schiller，STOC 2025]。但硬件中并无LL/SC，在我们的工作之前，尚未有具备类似特性的无等待或高效无锁软件实现的LL/SC。我们的工作表明，在合理假设m=Ω(n)的情况下，可在现有硬件上实现该哈希算法，且步复杂度和空间复杂度无渐近增长。
英文摘要
We study the fundamental problem of implementing $m$ linearizable LL/SC objects with constant expected step complexity in a system of $n$ processes, using bounded base objects commonly available in hardware. Assuming that each process may have at most $τ$ outstanding LL() operations, the best known deterministic algorithm requires $Ω(n^2τ+ m)$ base objects (CAS objects and registers) [Blelloch and Wei, DISC 2020]. Previously, no comparable randomized algorithm was known. By employing randomization and FADD objects in addition to CAS objects, we obtain a space bound of $O(nτ+m)$ against the weak adaptive adversary. For $m=O(1)$ this matches a lower bound for algorithms using CAS objects and registers [Aghazadeh and Woelfel, PODC 2015]. In addition, our object can be employed by quiescently history-independent (QHI) algorithms: Whenever no operation on the object is pending and no process has an outstanding LL() operation, its internal memory state is uniquely determined by the values of the $m$ LL/SC objects. An important application is a recent QHI dynamic hashing algorithm, which uses $Θ(m)$ hardware LL/SC objects to maintain a hash table of size $m$ [Attiya, Bender, Farach-Colton, Oshman, and Schiller, STOC 2025]. But LL/SC is not available in hardware, and prior to our work no wait-free or efficient lock-free software implementation of LL/SC with similar properties was known. Our work demonstrates that one can actually implement the hashing algorithm on available hardware, without an asymptotic increase in step and space complexity, under the reasonable assumption that $m=Ω(n)$.
CommentsFull version of the paper appearing in DISC 2026
