Article | Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society | Stronger Necessary Conditions for the Existence of a Compatible OSPF Metric

Title:
Stronger Necessary Conditions for the Existence of a Compatible OSPF Metric
Author:
Peter Broström: Link√∂ping Institute of Technology, Sweden Kaj Holmberg: Link√∂ping Institute of Technology, Sweden
Download:
Full text (pdf)
Year:
2004
Conference:
Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society
Issue:
014
Article no.:
016
No. of pages:
1
Publication type:
Abstract
Published:
2004-12-28
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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This presentation is a continuation of the presentation ‚ÄúDetermining the Non-Existence of a Compatible OSPF Metric‚ÄĚ. It addresses the question of whether or not for a set of desired traffic patterns in an Internet Protocol telecommunication network using OSPF (Open Shortest Path First); there exists a compatible metric; i.e. weights making the routers give the specified traffic patterns. In the previous presentation it was shown that the existence of what we here call 1-valid cycles prove the non-existence of a compatible metric. In a 1-valid cycle the flow of two commodities is changed in a cycle. We here prove that a 2-valid cycle; which is a cycle in which more than two commodities are changed; exists if and only if there exists a 1-valid cycle. Furthermore; a 3-valid set of cycles is defined as a set of cycles where the flow of one commodity is changed in each cycle. Unfortunately we have not been able to show that the non-existence of 3-valid sets of cycles is sufficient for the existence of a compatible metric. However; for some special cases; such as when the desired traffic patterns only consist of a number of trees; stronger results are obtainable. Since it is fairly easy to find 1-valid cycles; we also consider the case when we know that there does not exist any 1-valid cycle.

An alternate title of this talk is ‚ÄúIn Search of Sufficient Conditions for the Existence of a Compatible OSPF Metric‚ÄĚ. We can formulate sufficient conditions for the existence of a compatible metric; but at the moment this formulation is not practically usable. However; this talk aims to show that the gap between the necessary and sufficient conditions is decreasing.

Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society

Author:
Peter Broström, Kaj Holmberg
Title:
Stronger Necessary Conditions for the Existence of a Compatible OSPF Metric
References:
No references available

Nordic MPS 2004. The Ninth Meeting of the Nordic Section of the Mathematical Programming Society

Author:
Peter Broström, Kaj Holmberg
Title:
Stronger Necessary Conditions for the Existence of a Compatible OSPF Metric
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