Abstract
Broadcasting is an information dissemination problem in a connected network, in which one node, called the originator, disseminates a message to all other nodes by placing a series of calls along the communication lines of the network. Once informed, the nodes aid the originator in distributing the message. Finding the minimum broadcast time of a vertex in an arbitrary graph is NP-complete. The problem is solved polynomially only for trees. It is proved that the complexity of the problem of determining the minimum broadcast time of any vertex in an arbitrary tree T = (V, E) is Θ|V|. In this paper we present an algorithm that determines the broadcast time of any originator in an arbitrary unicyclic graph G = (V, E) in O(|V|) time. This, combined with the obvious lower bound, gives a Θ(|V|) solution for the problem of broadcasting in unicyclic graphs. As a byproduct, we also find a broadcast center of the unicyclic graph (a vertex in G with the minimum broadcast time).
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Harutyunyan, H., Maraachlian, E. (2007). Linear Algorithm for Broadcasting in Unicyclic Graphs. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_37
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DOI: https://doi.org/10.1007/978-3-540-73545-8_37
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