Top-k Graph Summarization on Hierarchical DAGs

Abstract

Directed acyclic graph (DAG) is an essentially important model to represent terminologies and their hierarchical relationships, such as Disease Ontology. Due to massive terminologies and complex structures in a large DAG, it is challenging to summarize the whole hierarchical DAG. In this paper, we study a new problem of finding k representative vertices to summarize a hierarchical DAG. To depict diverse summarization and important vertices, we design a summary score function for capturing vertices' diversity coverage and structure correlation. The studied problem is theoretically proven to be NP-hard. To efficiently tackle it, we propose a greedy algorithm with an approximation guarantee, which iteratively adds vertices with the large summary contributions into answers. To further improve answer quality, we propose a subtree extraction based method, which is proven to guarantee achieving higher-quality answers. In addition, we develop a scalable algorithm k-PCGS based on candidate pruning and DAG compression for large-scale hierarchical DAGs. Extensive experiments on large real-world datasets demonstrate both the effectiveness and efficiency of proposed algorithms.