Efficient and Effective Directed Minimum Spanning Tree Queries

Computing directed Minimum Spanning Tree (DMST) is a fundamental problem in graph theory. It is applied in a wide spectrum of fields from computer network and communication protocol design to revenue maximization in social networks and syntactic parsing in Natural Language Processing. State-of-the-art solutions are online algorithms that compute DMST for a given graph and a root. For multi-query requirements, the online algorithm is inefficient. To overcome the drawbacks, in this paper, we propose an indexed approach that reuses the computation result to facilitate single and batch queries. We store all the potential edges of DMST in a hierarchical tree in O(n) space complexity. Furthermore, we answer the DMST query of any root in O(n) time complexity. Experimental results demonstrate that our approach can achieve a speedup of 2–3 orders of magnitude in query processing compared to the state-of-the-art while consuming O(n) index size.