Generalizing Design of Support Measures for Counting Frequent Patterns in Graphs

Frequent subgraph mining (FSM) from graphs is an active subject in computer science research. One major challenge in FSM is the development of support measures, which are basically functions that map a pattern to its frequency count in a database. Current state-of-the-art in this topic features a hypergraph-based framework for modeling pattern occurrences which unifies the two main flavors of support measures: the overlap-graph based maximum independent set measure (MIS) and minimum image/instance based (MNI) measures. For the purpose of exploring the middle ground between these two groups and guiding the development of new support measures, we present general sufficient conditions for designing new support measures in hypergraph framework, which can be applied to MNI and other support measures that are not included in the overlap graph framework. We utilize the sufficient conditions to generalize MNI and minimum-instance measure (MI) for designing user-defined linear-time measures. Furthermore, we show that a maximum independent subedge set (MISS) measure developed from the sufficient conditions can fill the gap between MIS and MI in computation complexity and support count.