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Common-Flow Formulations for the Diameter Constrained Spanning and Steiner Tree Problems

In: Combinatorial Optimization and Applications

Author

Listed:
  • Luis Gouveia

    (Universidade de Lisboa, Faculdade de Ciências)

  • Markus Leitner

    (Vrije Universiteit Amsterdam)

  • Ivana Ljubić

    (ESSEC Business School)

Abstract

We consider the diameter constrained minimum Steiner tree problem on a graph (DCStTP). Given an edge-weighted undirected graph whose set of nodes is partitioned into a set of terminal and potential Steiner nodes, the objective is to find a minimum-weight subtree that spans all terminal nodes such that the number of hops between any two terminal nodes does not exceed a given diameter D. In this work, we introduce mixed-integer linear programming models for the DCStTP based on the concept of triangles, i.e. diameter constrained Steiner trees induced by terminal subsets of size three. Starting from a formulation that models a D-hop Steiner arborescence rooted at a randomly chosen terminal node, we discuss various possibilities of realizing triangles using multi-commodity, common, or uncommon flows. We analyse the strength of these models both theoretically and empirically, and investigate how their respective Benders reformulations influence the computational performance.

Suggested Citation

  • Luis Gouveia & Markus Leitner & Ivana Ljubić, 2024. "Common-Flow Formulations for the Diameter Constrained Spanning and Steiner Tree Problems," International Series in Operations Research & Management Science, in: Teodor Gabriel Crainic & Michel Gendreau & Antonio Frangioni (ed.), Combinatorial Optimization and Applications, pages 37-58, Springer.
    • Handle: RePEc:spr:isochp:978-3-031-57603-4_3
    DOI: 10.1007/978-3-031-57603-4_3
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