打破Longest Queue Drop竞争力的2倍壁垒
Breaking the Barrier of 2 for the Competitiveness of Longest Queue Drop
AI总结：
该研究针对共享内存交换机缓冲区管理问题，突破了长期以来Longest Queue Drop（LQD）算法竞争比为2的结论，证明其竞争比为1.6918，首次得到大于0的常数ε对应的(2−ε)上界。
摘要：
我们研究单位价值数据包共享内存交换机的缓冲区管理问题。共享内存交换机由一个输入端口、多个输出端口和一个具有特定容量的缓冲区组成。在每个时间步中，任意数量的数据包到达输入端口，每个数据包都发往一个输出端口，且被添加到对应输出端口的队列中。如果数据包总数超过缓冲区容量，就必须强制丢弃部分数据包。每个时间步结束时，每个输出端口发送其队列中的一个数据包，目标是最大化发送的数据包总数。\nLongest Queue Drop（LQD，最长队列丢弃）在线算法会接收所有到达缓冲区的数据包；但如果这导致缓冲区超出内存容量，LQD会从当前最长的队列中丢弃一个数据包，若存在并列最长的队列则任意选择。LQD算法于1991年首次提出，自2001年以来已知其竞争比为2。尽管LQD仍是该问题目前已知的最优在线算法且具有实用价值，但确定其真实竞争比是一个长期存在的开放问题。我们证明LQD的竞争比为1.6918，首次建立了LQD竞争比的(2−ε)上界，其中ε为大于0的常数。
英文摘要：
We consider the problem of managing the buffer of a shared-memory switch that transmits packets of unit value. A shared-memory switch consists of an input port, a number of output ports, and a buffer with a specific capacity. In each time step, an arbitrary number of packets arrive at the input port, each packet designated for one output port. Each packet is added to the queue of the respective output port. If the total number of packets exceeds the capacity of the buffer, some packets have to be irrevocably evicted. At the end of each time step, each output port transmits a packet in its queue and the goal is to maximize the number of transmitted packets. The Longest Queue Drop (LQD) online algorithm accepts any arriving packet to the buffer. However, if this results in the buffer exceeding its memory capacity, then LQD drops a packet from whichever queue is currently the longest, breaking ties arbitrarily. The LQD algorithm was first introduced in 1991, and is known to be $2$-competitive since 2001. Although LQD remains the best known online algorithm for the problem and is of practical interest, determining its true competitiveness is a long-standing open problem. We show that LQD is 1.6918-competitive, establishing the first $(2-\varepsilon)$ upper bound for the competitive ratio of LQD, for a constant $\varepsilon>0$.
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。
