In this paper, we consider contention resolution on a multiple-access communication channel. In this problem, a set of nodes arrive over time, each with a message it intends to send. In each time slot, each node may attempt to broadcast its message or remain idle. If a single node broadcasts in a slot, the message is received by all nodes; otherwise, if multiple nodes broadcast simultaneously, a collision occurs and none succeeds. If collision detection is available, nodes can differentiate collision and silence (i.e., no nodes broadcast). Performance of contention resolution algorithms is often measured by throughput -- the number of successful transmissions within a period of time; whereas robustness is often measured by jamming resistance -- a jammed slot always generates a collision. Previous work has shown, with collision detection, optimal constant throughput can be attained, even if a constant fraction of all slots are jammed. The situation when collision detection is not available, however, remains unclear. In a recent breakthrough paper [Bender et al., STOC '20], a crucial case is resolved: constant throughput is possible without collision detection, but only if there is no jamming. Nonetheless, the exact trade-off between the best possible throughput and the severity of jamming remains unknown. In this paper, we address this open question. Specifically, for any level of jamming ranging from none to constant fraction, we prove an upper bound on the best possible throughput, along with an algorithm attaining that bound. An immediate and interesting implication of our result is, when a constant fraction of all slots are jammed, which is the worst-case scenario, there still exists an algorithm achieving a decent throughput: $\Theta(t/\log{t})$ messages could be successfully transmitted within $t$ slots.

中文翻译：

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在没有冲突检测的情况下，争用解决方案之间的权衡取舍

在本文中，我们考虑了多址通信信道上的竞争解决。在此问题中，一组节点随时间到达，每个节点都带有要发送的消息。在每个时隙中，每个节点可以尝试广播其消息或保持空闲。如果单个节点在插槽中广播，则该消息将被所有节点接收；否则，如果多个节点同时广播，则会发生冲突，并且不会成功。如果冲突检测可用，则节点可以区分冲突和静默（即，不广播任何节点）。争用解决算法的性能通常通过吞吐量来衡量-一段时间内成功传输的次数；而坚固性通常是通过抗干扰性来衡量的-堵塞的插槽始终会产生碰撞。先前的工作显示了碰撞检测功能，即使所有时隙的恒定部分被卡住，也可以获得最佳的恒定吞吐量。但是，冲突检测不可用的情况仍然不清楚。在最近的突破性论文中[Bender等人，STOC '20]，解决了一个关键情况：没有碰撞检测，但只有在没有干扰的情况下，才能保持恒定的吞吐量。尽管如此，在最佳吞吐量和阻塞严重性之间的确切权衡仍然未知。在本文中，我们解决了这个悬而未决的问题。具体来说，对于从无到恒定分数的任何级别的干扰，我们证明了最佳吞吐量的上限，以及达到该上限的算法。我们的结果的直接和有趣的含义是，当所有插槽中有恒定的一部分被卡住时，这是最坏的情况，