Sur la complexité du routage OSPF

International audienceCe travail montre que dans un réseau (général) où le protocole de routage est OSPF avec la stratégie d'équilibrage de charge ECMP, le problème qui consiste à maximiser un flot simple d'une source vers un puits ne peut être approché à une constante près

On the complexity of equal shortest path routing

International audienceIn telecommunication networks packets are carried from a source s to a destination t on a path determined by the underlying routing protocol. Most routing protocols belong to the class of shortest path routing protocols. In such protocols, the network operator assigns a length to each link. A packet going from s to t follows a shortest path according to these lengths. For better protection and efficiency, one wishes to use multiple (shortest) paths between two nodes. Therefore the routing protocol must determine how the traffic from s to t is distributed among the shortest paths. In the protocol called OSPF-ECMP (for Open Shortest Path First-Equal Cost Multiple Path) the traffic incoming at every node is uniformly balanced on all outgoing links that are on shortest paths. In that context, the operator task is to determine the " best " link lengths, toward a goal such as maximizing the network throughput for given link capacities. In this work, we show that the problem of maximizing even a single commodity flow for the OSPF-ECMP protocol cannot be approximated within any constant factor ratio. Besides this main theorem, we derive some positive results which include polynomial-time approximations and an exponential-time exact algorithm

On the Hardness of Equal Shortest Path Routing

International audienceIn telecommunication networks packets are carried from a source s to a destination t on a path that is determined by the underlying routing protocol. Most routing protocols belong to the class of shortest path routing protocols. In such protocols, the network operator assigns a length to each link. A packet going from s to t follows a shortest path according to these lengths. For better protection and efficiency, one wishes to use multiple (shortest) paths between two nodes. Therefore the routing protocol must determine how the traffic from s to t is distributed among the shortest paths. In the protocol called ospf-ecmp (for Open Shortest Path First -Equal Cost Multiple Path) the traffic incoming at every node is uniformly balanced on all outgoing links that are on shortest paths. In that context, the operator task is to determine the "best" link lengths, toward a goal such as maximizing the network throughput for given link capacities. In this work, we show that the problem of maximizing even a single commodity flow for the ospf- ecmp protocol cannot be approximated within any constant factor ratio. Besides this main theorem, we derive some positive results which include polynomial-time approximations and an exponential-time exact algorithm. We also prove that despite their weakness, our approximation and exact algorithms are, in a sense, the best possible

Inapproximability results for the inverse shortest paths problem with integer lengths and unique shortest paths

We study the complexity of two Inverse Shortest Paths (ISP) problems with integer arc lengths and the requirement for uniquely determined shortest paths. Given a collection of paths in a directed graph, the task is to find positive integer arc lengths such that the given paths are uniquely determined shortest paths between their respective terminals. The first problem seeks for arc lengths that minimize the length of the longest of the prescribed paths. In the second problem, the length of the longest arc is to be minimized. We show that it is NP-hard to approximate the minimal longest path length within a factor less than 8/7 or the minimal longest arc length within a factor less than 9/8. This answers the (previously) open question whether these problems are NP-hard or not. We also present a simple algorithm that achieves an O(|V |)-approximation guarantee for both variants. Both ISP problems arise in the planning of telecommunication networks with shortest path routing protocols. Our results imply that it is NP-hard to decide whether a given path set can be realized with a real shortest path routing protocol such as OSPF, IS-IS, or RIP