Dendrogram Based Algorithm for Dominated Graph Flooding

In this paper, we are concerned with the problem of flooding undirected weighted graphs under ceiling constraints. We provide a new algorithm based on a hierarchical structure called dendrogram, which offers the significant advantage that it can be used for multiple flooding with various scenarios of the ceiling values. In addition, when exploring the graph through its dendrogram structure in order to calculate the flooding levels, independent subdendrograms are generated, thus offering a natural way for parallel processing. We provide an efficient implementation of our algorithm through suitable data structures and optimal organisation of the computations. Experimental results show that our algorithm outperforms well established classical algorithms, and reveal that the cost of building the dendrogram highly predominates over the total running time, thus validating both the efficiency and the hallmark of our method. Moreover, we exploit the potential parallelism exposed by the flooding procedure to design a multi-thread implementation. As the underlying parallelism is created on the fly, we use a queue to store the list of the sub-dendrograms to be explored, and then use a dynamic round-robin scheduling to assign them to the participating threads. This yields a load balanced and scalable process as shown by additional benchmark results. Our program runs in few seconds on an ordinary computer to flood graphs with more that 20 millions of nodes.