The recently developed dynamic discretization discovery (DDD) is a powerful method that allows many time-dependent problems to become more tractable. While DDD has been applied to a variety of problems, one particular challenge has been to deal with storage constraints without leading to a weak relaxation in each iteration. Specifically, the current approach to deal with certain hard storage constraints in continuous settings is to remove a subset of the storage constraints completely in each iteration of DDD. In this work, we show that for discrete problems, such weak relaxations are not necessary. Specifically, we find bounds on the additional storage that must be permitted in each iteration. We demonstrate our techniques in the case of the classical universal packet routing problem in the presence of bounded node storage, which can currently only be solved via integer programming. We present computational results demonstrating the effectiveness of DDD when solving universal packet routing.

翻译：近期发展的动态离散化发现（DDD）是一种强大的方法，能够使许多时间依赖问题更易于处理。尽管DDD已被应用于多种问题，但一个关键挑战在于处理存储约束时，如何在每次迭代中不导致松弛性减弱。具体而言，当前在连续场景中处理某些硬存储约束的方法，是在每次DDD迭代中完全移除部分存储约束。本研究表明，对于离散问题，这种弱松弛并非必要。我们确定了每次迭代中必须允许的附加存储的界限。以经典通用数据包路由问题为例，在存在有界节点存储的情况下，目前该问题仅能通过整数规划求解，我们展示了所提技术在其中的应用。计算结果验证了DDD在求解通用数据包路由问题时的有效性。