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：确定性网络（DetNet）是一种新兴技术，可在大型IP网络中提供确定性延迟和抖动以及在故障情况下零丢包。为了支持DetNet，我们必须能够为给定节点对找到一组满足延迟范围约束的低成本路由路径。然而，延迟范围约束路由（DRCR）问题是NP完全的。现有路由方法要么无法支持延迟范围约束，要么计算复杂度极高。我们提出Pulse$+$，一种高度可扩展且高效的DRCR问题求解器。Pulse$+$采用分支定界方法，并优化其剪枝策略以提高效率。我们还将Pulse$+$与分治方法相结合，提出CoSE-Pulse$+$，用于找到满足DetNet延迟范围和延迟差约束的一对主动/备份路径。Pulse$+$和CoSE-Pulse$+$均提供最优性保证。值得注意的是，尽管Pulse$+$和CoSE-Pulse$+$不具有多项式最坏情况时间复杂度，但其经验性能优越。我们使用在数千个节点和链路的网络上生成的合成测试用例，将Pulse$+$和CoSE-Pulse$+$与基于K-最短路径和拉格朗日对偶的算法进行了评估。Pulse$+$和CoSE-Pulse$+$均实现了显著的加速。为便于复现，我们在[1]中开源了代码和测试用例。