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Simple Greedy Algorithms for Fundamental Multidimensional Graph Problems

Author

Listed:
  • Vittorio Bilò

    (Università del Salento = University of Salento [Lecce])

  • Ioannis Caragiannis

    (Department of Computer Engineering and Informatics [Patras] - University of Patras)

  • Angelo Fanelli

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Michele Flammini

    (DI - Dipartimento di Informatica [Italy] - UNIVAQ - Università degli Studi dell'Aquila = University of L'Aquila = Université de L'Aquila)

  • Gianpiero Monaco

    (DI - Dipartimento di Informatica [Italy] - UNIVAQ - Università degli Studi dell'Aquila = University of L'Aquila = Université de L'Aquila)

Abstract

We revisit fundamental problems in undirected and directed graphs, such as the problems of computing spanning trees, shortest paths, steiner trees, and spanning arborescences of minimum cost. We assume that there are d different cost functions associated with the edges of the input graph and seek for solutions to the resulting multidimensional graph problems so that the p - norm of the different costs of the solution is minimized. We present combinatorial algorithms that achieve very good approximations for this objective. The main advantage of our algorithms is their simplicity: they are as simple as classical combinatorial graph algorithms of Dijkstra and Kruskal, or the greedy algorithm for matroids.

Suggested Citation

  • Vittorio Bilò & Ioannis Caragiannis & Angelo Fanelli & Michele Flammini & Gianpiero Monaco, 2017. "Simple Greedy Algorithms for Fundamental Multidimensional Graph Problems," Post-Print hal-02089412, HAL.
    • Handle: RePEc:hal:journl:hal-02089412
    DOI: 10.4230/LIPIcs.ICALP.2017.125
    Note: View the original document on HAL open archive server: https://hal.science/hal-02089412v1
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    References listed on IDEAS

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    1. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
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    1. Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2020. "Approximating combinatorial optimization problems with the ordered weighted averaging criterion," European Journal of Operational Research, Elsevier, vol. 286(3), pages 828-838.
    2. Baak, Werner & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2025. "Robust min-max (regret) optimization using ordered weighted averaging," European Journal of Operational Research, Elsevier, vol. 322(1), pages 171-181.

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