Graph-based algorithms for discovering a process model containing invisible tasks

An event log records the business processes of a company. Modeling event logs aim to help users in analyzing business processes. One of the problems in modeling event logs automatically is the addition of invisible tasks. Invisible tasks are dummy activities, other than activities of an event log, that are added to a process model to describe a correct process model. This research proposes a graph-based algorithm to mine the data from an event log. From the data, the graph-based algorithm establishes an additional-invisible-task process model by converting all of the processes in the event log into a link list and adding invisible tasks and operators for parallel relations, such as XOR Split or XOR Join. The experimental analysis explains that the fitness of the discovered process models by the graph-based algorithm was as high as that of compared algorithms, such as Alpha# models, Alpha$ models, CHMMNCIT models, and CHMM-IT models. Furthermore, the graph-based algorithm is more efficient than existing algorithms. This was proven by the time complexity of the graph-based, which is O(n ² ) while both of Alpha# and Alpha$ algorithm have a time complexity of O(n ⁴ ) and both of CHMM-IT and CHMM-NCIT algorithm have O(n ³ ).