The rainbow spanning forest problem
- 120 Downloads
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.
KeywordsGraph theory Edge-colored graph Rainbow components Multi-start scheme Heterochromatic components
Compliance with ethical standards
Conflict of interest
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.
- Carr RD, Doddi S, Konjedov G, Marathe M (2000) On the red-blue set cover problem. In: 11th ACN-SIAM symposium on discrete algorithms, pp 345–353Google Scholar
- Carrabs F, Cerrone C, Cerulli R (2014) A tabu search approach for the circle packing problem. In: 2014 17th International conference on network-based information systems. pp 165–171. IEEEGoogle Scholar
- Carrabs F, Cerrone C, Cerulli R, Silvestri S (March 2016) On the complexity of rainbow spanning forest problem. Technical Report 14922, Department od Mathematics, University of SalernoGoogle Scholar
- Cerrone C, Cerull R, Golden B (2017) Carousel greedy: a generalized greedy algorithm with applications in optimization. Comput Oper Res (submitted)Google Scholar
- Cerulli R, Fink A, Gentili M, Voß S (2005) Metaheuristics comparison for the minimum labelling spanning tree problem. In: The next wave in computing, optimization, and decision technologies. Springer, pp 93–106Google Scholar
- Chang RS, Leu SJ (1997) The minimum labeling spanning trees. Inf Process Lett 63:277–282Google Scholar
- Chen Y, Cornick N, Hall AO, Shajpal R, Silberholz J, Yahav I, Golden B (2008) Comparison of heuristics for solving the gmlst problem. In: Telecommunications modeling, policy, and technology. Springer, pp 191–217Google Scholar
- Fischetti M, Salazar González JJ, Toth P (1995) Experiments with a multi-commodity formulation for the symmetric capacitated vehicle routing problem. In: Proceedings of the 3rd meeting of the euro working group on transportation. pp 169–173Google Scholar
- Silvestri S, Laporte G, Cerulli R (2016) The rainbow cycle cover problem. Networks 68(4):260–270Google Scholar
- Xiong Y, Golden B, Wasil E (2007) The colorful traveling salesman problem. In: Extending the horizons: advances in computing, optimization, and decision technologies. Springer, pp 115–123Google Scholar
- Xiongm Y, Golden B, Wasil E, Chen S (2008) The label-constrained minimum spanning tree problem. In: Telecommunications modeling, policy, and technology, Springer, pp 39–58Google Scholar