缓解竞争解决中冲突的影响
Softening the Impact of Collisions in Contention Resolution
AI总结：
本文提出冲突规避退避（CAB）随机算法，同时优化竞争解决中的完工时间和冲突代价，在静态未知数据包数量下实现渐近最优性能，并给出公平算法的紧下界。
摘要：
竞争解决处理的是协调对共享通信信道访问的问题。时间被离散化为同步时隙，数据包可以在任何时隙发送。如果没有数据包发送，则该时隙为空；如果只发送一个数据包，则发送成功；而当多个数据包同时发送时，就会发生冲突，导致相应传输失败。在每个时隙中，每个数据包都会收到三元信道反馈，指示当前时隙是空、成功还是冲突。先前关于竞争解决的许多工作都集中在优化完工时间（makespan）上，即所有数据包成功所需的时隙数量。然而，在许多现代系统中，冲突在时间方面也会造成高昂的代价，而现有的竞争解决算法并未解决这一问题。在本文中，我们设计并分析了一种随机算法——冲突规避退避（Collision Aversion Backoff，CAB），该算法同时优化完工时间和冲突代价。我们考虑静态情况，即系统中初始存在未知的 $n\geq 2$ 个数据包，并且每次冲突具有已知代价 $\mathcal{C}$，其中 $1 \leq \mathcal{C} \leq n^κ$，$κ\geq 0$ 为已知常数。在关于 $n$ 的多项式级小的错误概率下，CAB 保证所有数据包成功，且完工时间和总期望冲突代价为 $\tilde{O}(n\sqrt{\mathcal{C}})$。我们给出了公平算法类别的下界：在公平算法中，在每个时隙，执行该算法的每个数据包以相同概率发送（且该概率可能随不同时隙而变化）。我们的下界在渐近意义上是紧的，对于足够大的 $\mathcal{C}$，紧致性达到 $\texttt{poly}(\log n)$ 因子范围内。
英文摘要：
Contention resolution addresses the problem of coordinating access to a shared communication channel. Time is discretized into synchronized slots, and a packet can be sent in any slot. If no packet is sent, then the slot is empty; if a single packet is sent, then it is successful; and when multiple packets are sent at the same time, a collision occurs, resulting in the failure of the corresponding transmissions. In each slot, every packet receives ternary channel feedback indicating whether the current slot is empty, successful, or a collision. Much of the prior work on contention resolution has focused on optimizing the makespan, which is the number of slots required for all packets to succeed. However, in many modern systems, collisions are also costly in terms of the time they incur, which existing contention-resolution algorithms do not address. In this paper, we design and analyze a randomized algorithm, Collision Aversion Backoff (CAB), that optimizes both the makespan and the collision cost. We consider the static case where an unknown $n\geq 2$ packets are initially present in the system, and each collision has a known cost $\mathcal{C}$, where $1 \leq \mathcal{C} \leq n^κ$ for a known constant $κ\geq 0$. With error probability polynomially small in $n$, CAB guarantees that all packets succeed with makespan and a total expected collision cost of $\tilde{O}(n\sqrt{\mathcal{C}})$. We give a lower bound for the class of fair algorithms: where, in each slot, every packet executing the fair algorithm sends with the same probability (and the probability may change from slot to slot). Our lower bound is asymptotically tight up to a $\texttt{poly}(\log n)$-factor for sufficiently large $\mathcal{C}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
