Abstract
In this paper we consider the following problem: Given a network G, determine if there is an edge in G through which at least c shortest paths pass. This problem arises naturally in various practical situations where there is a massive network (telephone, internet), and routing of data is done via shortest paths and one wants to identify most congested edges in the network.
This problem can be easily solved by one all pair shortest path computation which takes time O(mn), where n is the number of nodes and m the number of edges in the network. But for massive networks – can we do better? It seems hard to improve this bound by a deterministic algorithm and hence we naturally use randomization. The main contribution of this paper is to a give a practical solution (in time significantly less than O(mn)) to a problem of great importance in industry.
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Devanur, N., Lipton, R.J., Vishnoi, N. (2003). Who’sThe Weakest Link?. In: Albrecht, A., Steinhöfel, K. (eds) Stochastic Algorithms: Foundations and Applications. SAGA 2003. Lecture Notes in Computer Science, vol 2827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39816-5_10
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DOI: https://doi.org/10.1007/978-3-540-39816-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20103-8
Online ISBN: 978-3-540-39816-5
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