一种用于在线网络分组调度的常数近似算法
A Constant Approximation Algorithm for Scheduling Packets on Line Networks
摘要：
在本文中，我们改进的近似比的分组调度问题的有界缓冲区，其中的目标是最大化的吞吐量。网络中的每个节点具有有限大小的本地缓冲器$B$，并且每个边缘（或链路）可以在每个时间单元中传输有限数量的分组$c$。问题的输入由一组数据包请求组成，每个请求由源节点、目的节点和释放时间定义。我们用$n$表示网络的大小。这个问题的一个解决方案是一个时间表，提供（一些）数据包到他们的目的地，而不违反网络的容量限制（缓冲区或边缘）。我们的目标是设计一个有效的算法，计算一个时间表，最大限度地提高数据包到达各自的目的地。对于$B=Θ(c)$ .这改进了$O(\log^* n)$的先前最佳结果（Räcke和Rosén，Theory Comput.系统：49（4），2011）。我们的改进是基于一个新的组合引理，我们证明，说明，粗略地说，如果数据包被允许留在缓冲区中只有有限数量的时间步长，$2d$，其中$d$是最长的源-目的地距离的任何输入数据包，那么最佳解决方案的基数减少只有一个常数因子。这一主张以前在定向积分中是不知道的（即，不可分割的，0 - 1）情况，并且可以找到用于路由和调度算法的附加应用。
英文摘要：
In this paper we improve the approximation ratio for the problem of scheduling packets on line networks with bounded buffers, where the aim is that of maximizing the throughput. Each node in the network has a local buffer of bounded size $B$, and each edge (or link) can transmit a limited number, $c$, of packets in every time unit. The input to the problem consists of a set of packet requests, each defined by a source node, a destination node, and a release time. We denote by $n$ the size of the network. A solution for this problem is a schedule that delivers (some of the) packets to their destinations without violating the capacity constraints of the network (buffers or edges). Our goal is to design an efficient algorithm that computes a schedule that maximizes the number of packets that arrive to their respective destinations. We give a randomized approximation algorithm with constant approximation ratio for the case where $B=Θ(c)$. This improves over the previously best result of $O(\log^* n)$ (Räcke and Rosén, Theory Comput. Syst., 49(4), 2011). Our improvement is based on a new combinatorial lemma that we prove, stating, roughly speaking, that if packets are allowed to stay put in buffers only a limited number of time steps, $2d$, where $d$ is the longest source-destination distance of any input packet, then the cardinality of the optimal solution is decreased by only a constant factor. This claim was not previously known in the directed integral (i.e., unsplittable, zero-one) case, and may find additional applications for routing and scheduling algorithms.
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。
