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A Relax-And-Cut Algorithm For The Knapsack Node Weighted Steiner Tree Problem

Author

Listed:
  • ROBERTO CORDONE

    (DTI — Università degli Studi di Milano, via Bramante, 65, Crema, 26013, Italy)

  • MARCO TRUBIAN

    (DSI — Università degli Studi di Milano, via Comelico 39/41, Milano, 20135, Italy)

Abstract

TheKnapsack Node Weighted Steiner Tree Problem(KNWSTP) is a generalization of the Steiner Tree Problem on graphs, which takes into account the classical cost function defined on the edges, as well as a prize function defined on the vertices and a limit on the size of the solution. It has several applications to network design. We propose an exact branch-and-bound algorithm for this problem, based on a relax-and-cut approach: the algorithm relaxes an exponential family of generalized subtour elimination constraints and takes into account only the violated ones as the computation proceeds. The performance of the algorithm has been tested on a wide set of benchmark problems, up to three hundred vertices, whose structure reflects the features of the most likely applications (sparse graphs with Euclidean costs) and covers different cases with respect to the prize function (only positive, or both positive and negative prizes) and the weight threshold.

Suggested Citation

  • Roberto Cordone & Marco Trubian, 2008. "A Relax-And-Cut Algorithm For The Knapsack Node Weighted Steiner Tree Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 373-391.
    • Handle: RePEc:wsi:apjorx:v:25:y:2008:i:03:n:s0217595908001791
    DOI: 10.1142/S0217595908001791
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    Cited by:

    1. Fabio Colombo & Marco Trubian, 2014. "A column generation approach for Multicast Routing and Wavelength Assignment with Delay Constraints in heterogeneous WDM networks," Annals of Operations Research, Springer, vol. 222(1), pages 239-260, November.

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