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Augmenting weighted graphs to establish directed point-to-point connectivity

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Abstract

We consider an augmentation problem on undirected and directed graphs, where given a directed (an undirected) graph G and p pairs of vertices \(P=\left\{ {\left( {s_1 ,t_1 } \right) ,\ldots ,\left( {s_p ,t_p } \right) } \right\} \), one has to find the minimum weight set of arcs (edges) to be added to the graph so that the resulting graph has (can be oriented to have) directed paths between the specified pairs of vertices. In the undirected case, we present an FPT-algorithm with respect to the number of new edges. Also, we have implemented and evaluated the algorithm on some real-world networks to show its efficiency in decreasing the size of input graphs and converting them to much smaller kernels. In the directed case, we consider the complexity of the problem with respect to the various parameters and present some parameterized algorithms and parameterized complexity results for it.

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Acknowledgments

This research was in part supported by a grant from Institute for Research in Fundamental Sciences (IPM) (No. CS1395-4-01).

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Authors and Affiliations

  1. Department of Computer Engineering and Information Technology, AmirKabir University of Technology, P.O. Box 15875-4413, #424 Hafez Avenue, Tehran, Iran

    Mehdy Roayaei & Mohammadreza Razzazi

  2. School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

    Mohammadreza Razzazi

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  1. Mehdy Roayaei
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  2. Mohammadreza Razzazi
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Correspondence to Mohammadreza Razzazi.

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Roayaei, M., Razzazi, M. Augmenting weighted graphs to establish directed point-to-point connectivity. J Comb Optim 33, 1030–1056 (2017). https://doi.org/10.1007/s10878-016-0023-y

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