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Valid Cycles: A Source of Infeasibility in Open Shortest Path First Routing
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-5907-0087
2008 (English)In: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 52, no 4, 206-215 p.Article in journal (Refereed) Published
Abstract [en]

Many telecommunication networks use the open shortest path first (OSPF) protocol for the routing of traffic. In such networks, each router sends the traffic on the shortest paths to the destination, with respect to the link weights assigned. An interesting question is whether or not a set of desired routing patterns can be obtained in an OSPF network by assigning appropriate weights. If not, we wish to find the source of the infeasibility. We study these issues by formulating a mathematical model and investigating its feasibility. A certain structure, called valid cycle, is found to be present in most infeasible instances. This yields new necessary conditions, stronger than those previously known, for the existence of weights yielding a set of given desired shortest path graphs. A valid cycle indicates which parts of the routing patterns are in conflict and can be used for changing the routing patterns to make the problem feasible. A polynomial algorithm for finding valid cycles is presented, the method is illustrated by a numerical example, and computational tests are reported.

Place, publisher, year, edition, pages
2008. Vol. 52, no 4, 206-215 p.
Keyword [en]
telecommunication networks, Internet Protocol, OSPF, routing, compatible weights
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-53609DOI: 10.1002/net.20232OAI: oai:DiVA.org:liu-53609DiVA: diva2:290174
Available from: 2010-01-26 Created: 2010-01-26 Last updated: 2017-12-12

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Broström, PeterHolmberg, Kaj

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