Given an undirected and edge-colored graph G, a rainbow component of G is a subgraph of G having all the edges with different colors. The Rainbow Spanning Forest Problem consists of finding a spanning forest of G with the minimum number of rainbow components. The problem is known to be NP-hard on general graphs and on trees. In this paper, we present an integer linear mathematical formulation and a greedy algorithm to solve it. To further improve the results, we applied a multi-start scheme to the greedy algorithm. Computational results are reported on randomly generated instances.
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All authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
Communicated by V. Loia.
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Carrabs, F., Cerrone, C., Cerulli, R. et al. The rainbow spanning forest problem. Soft Comput 22, 2765–2776 (2018). https://doi.org/10.1007/s00500-017-2540-8