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.

The rainbow spanning forest problem

CARRABS, FRANCESCO;CERRONE, CARMINE
;
CERULLI, Raffaele;SILVESTRI, SELENE
2018-01-01

Abstract

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.
2018
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4681721
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