Deterministic Networking (DetNet) is a rising technology that offers deterministic delay \& jitter and zero packet loss regardless of failures in large IP networks. In order to support DetNet, we must be able to find a set of low-cost routing paths for a given node pair subject to delay-range constraints. Unfortunately, the \textbf{Delay-Range} Constrained Routing (DRCR) problem is NP-Complete. Existing routing approaches either cannot support the delay-range constraints, or incur extremely high computational complexity. We propose Pulse$+$, a highly scalable and efficient DRCR problem solver. Pulse$+$ adopts a branch-and-bound methodology and optimizes its pruning strategies for higher efficiency. We also integrate Pulse$+$ with a divide-and-conquer approach and propose CoSE-Pulse$+$ to find a pair of active/backup paths that meet DetNet's delay-range and delay-diff constraints. Both Pulse$+$ and CoSE-Pulse$+$ offer optimality guarantee. Notably, although Pulse$+$ and CoSE-Pulse$+$ do not have a polynomial worst-case time complexity, their empirical performance is superior. We evaluate Pulse$+$ and CoSE-Pulse$+$ against the K-Shorst-Path and Lagrangian-dual based algorithms using synthetic test cases generated over networks with thousands of nodes and links. Both Pulse$+$ and CoSE-Pulse$+$ achieve significant speedup. To enable reproduction, we open source our code and test cases at [1].

翻译：确定网络( DetNet) 是一个不断上升的技术, 提供确定延迟的延迟 <unk> jitter 和 零 包损失, 不论大型 IP 网络的失败。 为了支持 DetNet, 我们必须能够为特定节点配对找到一套低成本的路径路径, 但要受到延迟的制约。 不幸的是, 控制( DRCR) 问题是 NP- Compllete 。 现有的路由方法要么无法支持延迟的制约, 要么造成极高的计算复杂性。 我们建议 Pulse$+, 一个高度可缩放和高效的 DCR 问题解答器。 Pulse$+ 采用分支和约束的方法, 优化其节流战略, 并且用分化和制法的方法, 并提议COS- Pulce + COSe+ COSe 代码 + 来寻找一套符合Detreal- roupal roupal $ 美元 和 Excial- developal- deal- deal- develop $, 和Seal- developal- supal- developal- $+ cal- supal- suplateal- $ and a 和Ial- supal- suplational- supal- supal- supal- supal- supal- supal- supal- supal- supal- supal- $, $ 和 和 和SUlate- supal- suplational- supal- slational- supal- supal- supal- d- 和 和 和 和 和 和 和 +- supal- sil- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- supal- sal- sal- sal- sal- sal- sal- sal- sal- sal- sal- 和i- supal- 和i-</s>