Mining Preserving Structures in a Graph Sequence

Abstract

In the recent research of data mining, frequent structures in a sequence of graphs have been studied intensively, and one of the main concern is changing structures along a sequence of graphs that can capture dynamic properties of data. On the contrary, we newly focus on "preserving structures" in a graph sequence that satisfy a given property for a certain period, and mining such structures is studied. As for an onset, we bring up two structures, a connected vertex subset and a clique that exist for a certain period. We consider the problem of enumerating these structures. and present polynomial delay algorithms for the problems. Their running time may depend on the size of the representation, however, if each edge has at most one time interval in the representation, the running time is O(|V ||E| 3 ) for connected vertex subsets and O(min{∆ 5 , |E| 2 ∆}) for cliques, where the input graph is G = (V, E) with maximum degree ∆. To the best of our knowledge, this is the first approach to the treatment of this notion, namely, preserving structures. ⋆

Adapting the Bron–Kerbosch algorithm for enumerating maximal cliques in temporal graphs

“…Indeed, clique finding is a special case of dense subgraph detection. Second, more recently, mining dynamic or temporal networks for periodic interactions [17] or preserving structures [26] (in particular, this may include cliques as a very fundamental pattern) has gained increased attention. Our work is directly motivated by the study of Viard et al [28,29] who introduced the concept of ∆-cliques and provided a corresponding enumeration algorithm for ∆-cliques.…”

PSpan:Mining Frequent Subnets of Petri Nets

“…However, most existing FSM algorithms are designed for specific datasets, such as biological datasets and molecular datasets [36,13,5]. Some additional constraints, such as closeness, maximal, gap satisfaction, particular structure, and community property, have been added to accelerate the computation [48,3,23,49,56]. There have been works improving gSpan [28].…”