In this paper, we consider the Delay Constrained Unsplittable Shortest Path Routing problem which arises in the field of traffic engineering for IP networks. This problem consists, given a directed graph and a set of commodities, to compute a set of routing paths and the associated administrative weights such that each commodity is routed along the unique shortest path between its origin and its destination, according to these weights. We present a compact MILP formulation for the problem, extending the work in (A. Bley, 2010) along with some valid inequalities to strengthen its linear relaxation. This formulation is used as the bulding block of an iterative approach that we develop to tackle large scale instances. We further propose a dynamic programming algorithm based on a tree decomposition of the graph. To the best of our knowledge, this is the first exact combinatorial algorithm for the problem. Finally, we assess the efficiency of our approaches through a set of experiments on state-of-the-art instances.

中文翻译：

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不可分割的最短路径路由问题的可扩展算法

在本文中，我们考虑了 IP 网络流量工程领域中出现的延迟约束不可拆分最短路径路由问题。这个问题包括，给定一个有向图和一组商品，计算一组路由路径和相关的管理权重，以便根据这些权重，每个商品都沿着其起点和目的地之间的唯一最短路径进行路由。我们针对该问题提出了一个紧凑的 MILP 公式，扩展了 (A. Bley, 2010) 中的工作以及一些有效的不等式以加强其线性松弛。这个公式被用作我们开发的迭代方法的构建块，以解决大规模实例。我们进一步提出了一种基于图的树分解的动态规划算法。据我们所知，这是该问题的第一个精确组合算法。最后，我们通过对最先进实例的一组实验来评估我们方法的效率。