Sequential visibility-graph motifs

Visibility graph motifs

Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of visibility graph motifs, smaller substructures that appear with characteristic frequencies. We develop ...

Epileptic seizure detection based on The Limited Penetrable visibility graph algorithm and graph properties

Introduction: Epileptic seizure detection is a key step for both researchers and epilepsy specialists for epilepsy assessment due to the non-stationariness and chaos in the electroencephalogram (EEG) signals. Current research is directed toward the development of an efficient method for epilepsy or seizure detection based the limited penetrable visibility graph (LPVG) algorith...

Probably Optimal Graph Motifs

We show an O∗(2k)-time polynomial space algorithm for the k-sized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute, and Min-Add. Moreover, we provide a piece of ...

Routing on the Visibility Graph

We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let P be a set of n points in the plane and let S be a set of non-crossing line segments whose endpoints are in P . We present two deterministic 1-local O(1)-memory routing algorithms that are guaranteed to find a path of at most linea...

Visibility Graph of a Set of Line Sements: A Dynamic Sequential Algorithm and Its Parallel Version