高效的随机化测试集实现
Efficient Randomized Test-And-Set Implementations
摘要：
我们研究随机测试和设置（TAS）的实现从寄存器中的异步共享内存模型与n个进程。我们介绍了组选举的问题，领导选举的自然变种，并提出了一个框架，从组选举对象的TAS对象的实现。然后，我们提出了两个组选举算法，每个产生一个有效的TAS实现。第一种实现在位置不经意攻击者模型中具有预期的最大步长复杂度$O(\log^\ast k)$，第二种实现具有针对任何读/写不经意攻击者的预期的最大步长复杂度$O(\log\log k)$，其中$k\leq n$是竞争。这些算法改进了Alistarh和Aspnes [2]提出的$O(\log\log n)$期望最大步复杂度的上界。我们还针对强自适应对手提出了对Alistarh，Attiya，Gilbert，Giurgiu和Guerraoui [5]的TAS算法的修改，将其空间复杂度从超线性提高到线性，同时保持其$O(\log n)$预期的最大步长复杂度。然后，我们描述了如何将该算法与任何随机TAS算法相结合，预期最大步的复杂性$T(n)$在一个较弱的对手模型，使所得到的算法有$O(\log n)$预期最大步的复杂性对任何强的自适应对手和$O(T(n))$在较弱的对手模型。最后，证明了对于任意随机2进程TAS算法，存在一个由不经意对手确定的调度，使得至少有$(1/4)^t$一个进程至少需要t步才能完成其TAS操作.这补充了Attiya和Censor-Hillel [7]关于$n\geq 3$过程的类似问题的下界。
英文摘要：
We study randomized test-and-set (TAS) implementations from registers in the asynchronous shared memory model with n processes. We introduce the problem of group election, a natural variant of leader election, and propose a framework for the implementation of TAS objects from group election objects. We then present two group election algorithms, each yielding an efficient TAS implementation. The first implementation has expected max-step complexity $O(\log^\ast k)$ in the location-oblivious adversary model, and the second has expected max-step complexity $O(\log\log k)$ against any read/write-oblivious adversary, where $k\leq n$ is the contention. These algorithms improve the previous upper bound by Alistarh and Aspnes [2] of $O(\log\log n)$ expected max-step complexity in the oblivious adversary model. We also propose a modification to a TAS algorithm by Alistarh, Attiya, Gilbert, Giurgiu, and Guerraoui [5] for the strong adaptive adversary, which improves its space complexity from super-linear to linear, while maintaining its $O(\log n)$ expected max-step complexity. We then describe how this algorithm can be combined with any randomized TAS algorithm that has expected max-step complexity $T(n)$ in a weaker adversary model, so that the resulting algorithm has $O(\log n)$ expected max-step complexity against any strong adaptive adversary and $O(T(n))$ in the weaker adversary model. Finally, we prove that for any randomized 2-process TAS algorithm, there exists a schedule determined by an oblivious adversary such that with probability at least $(1/4)^t$ one of the processes needs at least t steps to finish its TAS operation. This complements a lower bound by Attiya and Censor-Hillel [7] on a similar problem for $n\geq 3$ processes.
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