Proceedings of the 2005 ACM symposium on Applied computing
Computing optimal max-min fair resource allocation for elastic flows
IEEE/ACM Transactions on Networking (TON)
A CP-LP approach to network management in OSPF routing
Proceedings of the 2007 ACM symposium on Applied computing
On shortest path representation
IEEE/ACM Transactions on Networking (TON)
An Integer Programming Algorithm for Routing Optimization in IP Networks
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A new necessary condition for shortest path routing
NET-COOP'07 Proceedings of the 1st EuroFGI international conference on Network control and optimization
Complexity of inverse shortest path routing
INOC'11 Proceedings of the 5th international conference on Network optimization
On the approximability of the minimum congestion unsplittable shortest path routing problem
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Two mathematically equivalent models of the unique-path OSPF weight setting problem
ICN'05 Proceedings of the 4th international conference on Networking - Volume Part II
Modelling and constraint hardness characterisation of the unique-path OSPF weight setting problem
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
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In most domains of the Internet network, the traffic demands are routed on a single-path defined as the shortest one according to a set of administrative weights. Most of the time, the values set by the administrator (or the default ones) are such that there are many paths of the same length between the extremities of some demands. However, if the shortest paths are not unique, it might become difficult for an Internet domain administrator to predict and control the traffic flows in the network. Moreover, the sequence order of packets can be changed when many paths are used leading to some end-to-end delays. It is hence an important issue to ensure that each shortest path is unique according to a given set of administrative weights. We show that it is possible to determine a set of small integer weights (smaller than 6 times the radius of the network) such that all links are used and every demand is routed on a unique shortest path. Above and beyond this uniqueness requirement, network administrators wishing to exploit the available resources would like to control the whole routing pattern. The problem they face consists of determining a set of weights enforcing a given routing policy. We formulate this problem using linear programs, and we show how integer weights can be computed by heuristics with guaranteed worst-case performances. Some conditions on the given routing, necessary for the existence of a solution, are derived. Both necessary and sufficient conditions are also provided, together with some other useful properties, in the case of particular graphs such as cycles and cacti.