In the Contention Resolution problem $n$ parties each wish to have exclusive use of a shared resource for one unit of time. The problem has been studied since the early 1970s, under a variety of assumptions on feedback given to the parties, how the parties wake up, knowledge of $n$, and so on. The most consistent assumption is that parties do not have access to a global clock, only their local time since wake-up. This is surprising because the assumption of a global clock is both technologically realistic and algorithmically interesting. It enriches the problem, and opens the door to entirely new techniques. Our primary results are: [1] We design a new Contention Resolution protocol that guarantees latency $$O\left(\left(n\log\log n\log^{(3)} n\log^{(4)} n\cdots \log^{(\log^* n)} n\right)\cdot 2^{\log^* n}\right) \le n(\log\log n)^{1+o(1)}$$ in expectation and with high probability. This already establishes at least a roughly $\log n$ complexity gap between randomized protocols in GlobalClock and LocalClock. [2] Prior analyses of randomized ContentionResolution protocols in LocalClock guaranteed a certain latency with high probability, i.e., with probability $1-1/\text{poly}(n)$. We observe that it is just as natural to measure expected latency, and prove a $\log n$-factor complexity gap between the two objectives for memoryless protocols. The In-Expectation complexity is $Θ(n \log n/\log\log n)$ whereas the With-High-Probability latency is $Θ(n\log^2 n/\log\log n)$. Three of these four upper and lower bounds are new. [3] Given the complexity separation above, one would naturally want a ContentionResolution protocol that is optimal under both the In-Expectation and With-High-Probability metrics. This is impossible! It is even impossible to achieve In-Expectation latency $o(n\log^2 n/(\log\log n)^2)$ and With-High-Probability latency $n\log^{O(1)} n$ simultaneously.

翻译：在竞争解决（Contention Resolution）问题中，$n$ 个参与方各自希望独占使用一个共享资源一个单位时间。自 20 世纪 70 年代初以来，该问题已在多种假设下被研究，包括反馈给参与方的信息、参与方的唤醒方式、对 $n$ 的了解程度等。最一致的假设是参与方无法访问全局时钟，只能依赖自唤醒以来的本地时间。这令人惊讶，因为全局时钟的假设不仅在技术上现实，而且在算法上具有研究价值。它丰富了问题内涵，并开启了全新的技术路径。我们的主要成果如下：[1] 我们设计了一种新的竞争解决协议，其延迟在期望值和高概率下均满足 $$O\left(\left(n\log\log n\log^{(3)} n\log^{(4)} n\cdots \log^{(\log^* n)} n\right)\cdot 2^{\log^* n}\right) \le n(\log\log n)^{1+o(1)}$$。这已初步证明在 GlobalClock 与 LocalClock 模型下的随机化协议之间至少存在约 $\log n$ 的复杂度差距。[2] 先前对 LocalClock 模型中随机化竞争解决协议的分析仅保证高概率（即概率 $1-1/\text{poly}(n)$）下的特定延迟。我们指出，衡量期望延迟同样自然，并证明了无记忆协议在这两种目标之间存在 $\log n$ 因子的复杂度差距：期望复杂度为 $Θ(n \log n/\log\log n)$，而高概率延迟为 $Θ(n\log^2 n/\log\log n)$。这四个上下界中有三个是新的。[3] 基于上述复杂度分离，人们自然希望获得一种在期望延迟和高概率延迟两个指标下均最优的竞争解决协议。但这是不可能的！甚至无法同时实现 $o(n\log^2 n/(\log\log n)^2)$ 的期望延迟和 $n\log^{O(1)} n$ 的高概率延迟。