We consider several basic questions on distributed routing in directed graphs with multiple additive costs, or metrics, and multiple constraints. Distributed routing in this sense is used in several protocols, such as IS-IS and OSPF. A practical approach to the multi-constraint routing problem is to, first, combine the metrics into a single `composite' metric, and then apply one-to-all shortest path algorithms, e.g. Dijkstra, in order to find shortest path trees. We show that, in general, even if a feasible path exists and is known for every source and destination pair, it is impossible to guarantee a distributed routing under several constraints. We also study the question of choosing the optimal `composite' metric. We show that under certain mathematical assumptions we can efficiently find a convex combination of several metrics that maximizes the number of discovered feasible paths. Sometimes it can be done analytically, and is in general possible using what we call a 'smart iterative approach'. We illustrate these findings by extensive experiments on several typical network topologies.

翻译：本文研究了具有多个加性代价（或度量）与多个约束的有向图中分布式路由的几个基本问题。此类分布式路由被应用于IS-IS和OSPF等协议中。多约束路由问题的实用方法是，首先将多个度量合并为单个“复合”度量，然后应用单源最短路径算法（如Dijkstra）寻找最短路径树。我们证明，一般情况下，即使每条源-目的对之间均存在且已知可行路径，也无法保证在多个约束下的分布式路由。我们还研究了最优“复合”度量的选择问题。结果表明，在特定数学假设下，我们可以高效地找到多个度量的凸组合，使发现的可行路径数量最大化。这种组合有时可通过解析方法实现，而一般情况下则可借助我们称为“智能迭代方法”的技术完成。我们通过在若干典型网络拓扑上的大量实验验证了这些结论。