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

Author

Listed:
  • Mehdy Roayaei

    (AmirKabir University of Technology)

  • Mohammadreza Razzazi

    (AmirKabir University of Technology
    School of Computer Science, Institute for Research in Fundamental Sciences (IPM))

Abstract

We consider an augmentation problem on undirected and directed graphs, where given a directed (an undirected) graph G and p pairs of vertices $$P=\left\{ {\left( {s_1 ,t_1 } \right) ,\ldots ,\left( {s_p ,t_p } \right) } \right\} $$ P = s 1 , t 1 , … , s p , t p , 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.

Suggested Citation

  • Mehdy Roayaei & Mohammadreza Razzazi, 2017. "Augmenting weighted graphs to establish directed point-to-point connectivity," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 1030-1056, April.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:3:d:10.1007_s10878-016-0023-y
    DOI: 10.1007/s10878-016-0023-y
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    References listed on IDEAS

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    1. Harold N. Gabow & Tibor Jordán, 2000. "Incrementing Bipartite Digraph Edge-Connectivity," Journal of Combinatorial Optimization, Springer, vol. 4(4), pages 449-486, December.
    2. Janny M. Y. Leung & Thomas L. Magnanti & Vijay Singhal, 1990. "Routing in Point-to-Point Delivery Systems: Formulations and Solution Heuristics," Transportation Science, INFORMS, vol. 24(4), pages 245-260, November.
    3. Refael Hassin & Jérôme Monnot & Danny Segev, 2007. "Approximation algorithms and hardness results for labeled connectivity problems," Journal of Combinatorial Optimization, Springer, vol. 14(4), pages 437-453, November.
    4. Danny Segev, 2011. "Approximating k-generalized connectivity via collapsing HSTs," Journal of Combinatorial Optimization, Springer, vol. 21(3), pages 364-382, April.
    5. Da Huang & Zhao Zhang, 2012. "On cyclic vertex-connectivity of Cartesian product digraphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 379-388, October.
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