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New graph colouring algorithm for resource allocation in large-scale wireless networks

The vertex-colouring problem is a well-known classical problem in graph theory in which a colour is assigned to each vertex of the graph such that no two adjacent vertices have the same colour. The minimum vertex-colouring problem is known as NP-hard problem in an arbitrary graph. In this paper a graph colouring algorithm based on modified incidence matrix is proposed for resolving Physical Cell ID (PCI) allocation for large-scale femtocell deployment in LTE Telecommunication Networks. The proposed algorithm is not specified for neighbours only, but additionally can deal with neighbours of neighbours' objects due to telecommunication requirements. Our results show that by applying proper searching and assigning methods it is possible to achieve satisfactory results for resource allocation in large and complex networks such as resolving PCI allocation and conflict for large femtocells deployment in LTE Networks.