Abstract
We presented in [12] an algorithm for computing a parameter called T -interval connectivity of dynamic graphs which are given as a sequence of static graphs. This algorithm operates at a high level, manipulating the graphs in the sequence as atomic elements with two types of operations: a composition operation and a test operation. The algorithm is optimal in the sense that it uses only \(O(\delta )\) composition and test operations, where \(\delta \) is the length of the sequence. In this paper, we generalize this framework to use various composition and test operations, which allows us to compute other parameters using the same high-level strategy that we used for T-interval connectivity. We illustrate the framework through the study of three minimization problems which refer to various properties of dynamic graphs, namely Bounded-Realization-of-the-Footprint, Temporal-Connectivity, and Round-Trip-Temporal-Diameter.
Part of this work was done while Joseph Peters was visiting the LaBRI as a guest professor of the University of Bordeaux. This work was partially funded by the ANR projects DISPLEXITY (ANR-11-BS02-014) and ESTATE (ANR-16-CE25-0009-03). This study has been carried out in the frame of “The Investments for the Future” Programme IdEx Bordeaux CPU (ANR-10-IDEX-03-02). The work of Joseph Peters was partially supported by NSERC of Canada.
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Casteigts, A., Klasing, R., Neggaz, Y.M., Peters, J.G. (2017). A Generic Framework for Computing Parameters of Sequence-Based Dynamic Graphs. In: Das, S., Tixeuil, S. (eds) Structural Information and Communication Complexity. SIROCCO 2017. Lecture Notes in Computer Science(), vol 10641. Springer, Cham. https://doi.org/10.1007/978-3-319-72050-0_19
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