Computing Parameters of Sequence-Based Dynamic Graphs
Theory of Computing Systems \/ Mathematical Systems Theory(2018)
摘要
We present a general framework for computing parameters of dynamic networks which are modelled as a sequence 𝒢=(G_1,G_2,… ,G_δ) of static graphs such that G_i=(V,E_i) represents the network topology at time i and changes between consecutive static graphs are arbitrary. The framework 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 framework allows us to compute different parameters of dynamic graphs using a common high-level strategy by using composition and test operations that are specific to the parameter. The resulting algorithms are optimal in the sense that they use only O(δ ) composition and test operations, where δ is the length of the sequence. We illustrate our framework with three minimization problems, bounded realization of the footprint, temporal diameter, and round trip temporal diameter, and with T-interval connectivity which is a maximization problem. We prove that the problems are in NC by presenting polylogarithmic-time parallel versions of the algorithms. Finally, we show that the algorithms can operate online with amortized complexity Θ(1) composition and test operations for each graph in the sequence.
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关键词
Dynamic networks, Property testing, Generic algorithms, Temporal connectivity
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