Sliding Suffix Tree google
We consider a sliding window over a stream of characters from some finite alphabet. The user wants to perform deterministic substring matching on the current sliding window content and obtain positions of the matches. We present an indexed version of the sliding window based on a suffix tree. The data structure has optimal time queries $\Theta(m+occ)$ and amortized constant time updates, where $m$ is the length of the query string and $occ$ the number of occurrences. …

KlusTree google
Graph structured data on the web is now massive as well as diverse, ranging from social networks, web graphs to knowledge-bases. Effectively querying this graph structured data is non-trivial and has led to research in a variety of directions — structured queries, keyword and natural language queries, automatic translation of these queries to structured queries, etc. We are concerned with a class of queries called relationship queries, which are usually expressed as a set of keywords (each keyword denoting a named entity). The results returned are a set of ranked trees, each of which denotes relationships among the various keywords. The result list could consist of hundreds of answers. The problem of keyword search on graphs has been explored for over a decade now, but an important aspect that is not as extensively studied is that of user experience. We propose KlusTree, which presents clustered results to the users instead of a list of all the results. In our approach, the result trees are represented using language models and are clustered using JS divergence as a distance measure. We compare KlusTree with the well-known approaches based on isomorphism and tree-edit distance based clustering. The user evaluations show that KlusTree outperforms the other two in providing better clustering, thereby enriching user experience, revealing interesting patterns and improving result interpretation by the user. …

Graph sketching-based Massive Data Clustering (DBMSTClu) google
In this paper, we address the problem of recovering arbitrary-shaped data clusters from massive datasets. We present DBMSTClu a new density-based non-parametric method working on a limited number of linear measurements i.e. a sketched version of the similarity graph $G$ between the $N$ objects to cluster. Unlike $k$-means, $k$-medians or $k$-medoids algorithms, it does not fail at distinguishing clusters with particular structures. No input parameter is needed contrarily to DBSCAN or the Spectral Clustering method. DBMSTClu as a graph-based technique relies on the similarity graph $G$ which costs theoretically $O(N^2)$ in memory. However, our algorithm follows the dynamic semi-streaming model by handling $G$ as a stream of edge weight updates and sketches it in one pass over the data into a compact structure requiring $O(\operatorname{poly} \operatorname{log} (N))$ space. Thanks to the property of the Minimum Spanning Tree (MST) for expressing the underlying structure of a graph, our algorithm successfully detects the right number of non-convex clusters by recovering an approximate MST from the graph sketch of $G$. We provide theoretical guarantees on the quality of the clustering partition and also demonstrate its advantage over the existing state-of-the-art on several datasets. …

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