https://scigraph.springernature.com/explorer/license/
http://link.springer.com/10.1007/978-3-319-21398-9_1
2015
en
chapter
false
2019-04-15T19:11
Mining Preserving Structures in a Graph Sequence
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. We bring up two structures of practical importance, 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 \(O(\min \{\Delta ^5, |E|^2 \Delta \})\) for cliques, where the input graph is \(G=(V, E)\) with maximum degree \(\Delta \). To the best of our knowledge, this is the first systematic approach to the treatment of this notion, namely, preserving structures.
2015-01-01
chapters
3-15
Information and Computing Sciences
Xu
Dachuan
Takeaki
Uno
Dingzhu
Du
Springer Nature - SN SciGraph project
Du
Donglei
Yushi
Uno
978-3-319-21397-2
Computing and Combinatorics
978-3-319-21398-9
dimensions_id
pub.1039536391
National Institute of Informatics
National Institute of Informatics
readcube_id
bc5548caac2446309d9120ec022e6474e4c14a79cb71003b99aeeb326f470f4a
Springer International Publishing
Cham
Osaka Prefecture University
Graduate School of Science, Osaka Prefecture University
Computation Theory and Mathematics
10.1007/978-3-319-21398-9_1
doi