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Preprint 025-2009

Logarithmic inapproximability results for the minimum shortest path routing conflict problem

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Author(s) : Andreas Bley

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 025-2009

MSC 2000

90C60 Abstract computational complexity for mathematical programming problems
90B18 Communication networks

Abstract :
Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set S of routing paths forms a valid routing and, if this is not the case, to find a small subset R of paths that cannot occur together in any valid routing. In this paper we show that it is NP-hard to approximate the minimal size or the minimal weight of a shortest path conflict $R\subseteq S$ by a factor less than $c\log |S|$ for some $c>0$.

Keywords : shortest path routing, computational complexity

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