无冲突检测的竞争解决方案中的紧密权衡
Tight Trade-off in Contention Resolution without Collision Detection
摘要：
在本文中，我们考虑竞争解决多址通信信道。在这个问题中，一组节点随着时间的推移到达，每个节点都有一条它打算发送的消息。在每个时隙中，每个节点可以尝试广播其消息或保持空闲。如果单个节点在时隙中广播，则消息被所有节点接收;否则，如果多个节点同时广播，则发生冲突并且没有成功。如果冲突检测可用，则节点可以区分冲突和静默（即，没有节点广播）。竞争解决算法的性能通常由吞吐量（在一段时间内成功传输的次数）来衡量;而鲁棒性通常由抗干扰性来衡量，被干扰的时隙总是会产生冲突。以前的工作已经表明，冲突检测，最佳的恒定吞吐量可以达到，即使一个恒定的分数的所有插槽堵塞。然而，碰撞检测不可用时的情况仍不清楚。在最近的一篇突破性论文[Bender等人，STOC '20]，解决了一个关键的情况：恒定的吞吐量是可能的，没有冲突检测，但只有当没有干扰。尽管如此，最佳吞吐量和干扰严重性之间的确切权衡仍然未知。在本文中，我们解决这个开放的问题。具体来说，对于任何水平的干扰范围从没有到恒定的分数，我们证明了最好的可能的吞吐量的上限，以及实现该界限的算法。我们的结果的一个直接和有趣的含义是，当所有时隙的一个常数部分被堵塞，这是最坏的情况下，仍然存在一个算法实现了体面的吞吐量：$Θ(t/\log{t})$消息可以成功地在$t$时隙内传输。
英文摘要：
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: $Θ(t/\log{t})$ messages could be successfully transmitted within $t$ slots.
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