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Data summarization that presents a small subset of a dataset to users hasbeen widely applied in numerous applications and systems. Many datasets arecoded with hierarchical terminologies, e.g., the international classificationof Diseases-9, Medical Subject Heading, and Gene Ontology, to name a few. Inthis paper, we study the problem of selecting a diverse set of k elements tosummarize an input dataset with hierarchical terminologies, and visualize thesummary in an ontology structure. We propose an efficient greedy algorithm tosolve the problem with (1-1/e) = 62% -approximation guarantee. Although thisgreedy solution achieves quality-guaranteed answers approximately but it isstill not optimal. To tackle the problem optimally, we further develop adynamic programming algorithm to obtain optimal answers for graph visualizationof log-data using ontology terminologies called OVDO . The complexity andcorrectness of OVDO are theoretically analyzed. In addition, we propose auseful optimization technique of tree reduction to remove useless nodes withzero weights and shrink the tree into a smaller one, which ensures theefficiency acceleration of OVDO in many real-world applications. Extensiveexperimental results on real-world datasets show the effectiveness andefficiency of our proposed approximate and exact algorithms for tree datasummarization.

Efficient and Optimal Algorithms for Tree Summarization with Weighted Terminologies