Bipartite graph search optimization for type II diabetes mellitus Jamu formulation using branch and bound algorithm

Jamu is an Indonesian traditional herbal medicine that has been practiced for generations. Jamu is made from various medicinal plants. Each plant has several compounds directly related to the target protein that are directly associated with a disease. A pharmacological graph can form relationships between plants, compounds, and target proteins. Research related to the prediction of Jamu formulas for some diseases has been carried out, but there are problems in finding combinations or compositions of Jamu formulas because of the increase in search space size. Some studies adopted the drug–target interaction (DTI) implemented using machine learning or deep learning to predict the DTI for discovering the Jamu formula. However, this approach raises important issues, such as imbalanced and high-dimensional dataset, overfitting, and the need for more procedures to trace compounds to their plants. This study proposes an alternative approach by implementing bipartite graph search optimization using the branch and bound algorithm to discover the combination or composition of Jamu formulas by optimizing the search on a plant–protein bipartite graph. The branch and bound technique is implemented using the search strategy of breadth first search (BrFS), Depth First Search, and Best First Search. To show the performance of the proposed method, we compared our method with a complete search algorithm, searching all nodes in the tree without pruning. In this study, we specialize in applying the proposed method to search for the Jamu formula for type II diabetes mellitus (T2DM). The result shows that the bipartite graph search with the branch and bound algorithm reduces computation time up to 40 times faster than the complete search strategy to search for a composition of plants. The binary branching strategy is the best choice, whereas the BrFS strategy is the best option in this research. In addition, the the proposed method can suggest the composition of one to four plants for the T2DM Jamu formula. For a combination of four plants, we obtain Angelica Sinensis, Citrus aurantium, Glycyrrhiza uralensis, and Mangifera indica. This approach is expected to be an alternative way to discover the Jamu formula more accurately.