Growing Graphs with Hyperedge Replacement Graph Grammars

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering from the extraction process, the extracted graph grammar is guaranteed to generate an isomorphic copy of the original graph. Or, a stochastic application of the graph grammar rules can be used to quickly create random graphs. In experiments on large real world networks, we show that random graphs, generated from extracted graph grammars, exhibit a wide range of properties that are very similar to the original graphs. In addition to graph properties like degree or eigenvector centrality, what a graph "looks like" ultimately depends on small details in local graph substructures that are difficult to define at a global level. We show that our generative graph model is able to preserve these local substructures when generating new graphs and performs well on new and difficult tests of model robustness.Comment: 18 pages, 19 figures, accepted to CIKM 2016 in Indianapolis, I

Characterizing Compressibility of Disjoint Subgraphs with NLC Grammars

We consider compression of a given set S of isomorphic and disjoint subgraphs of a graph G using node label controlled (NLC) graph grammars. Given S and G, we characterize whether or not there exists a NLC graph grammar consisting of exactly one rule such that (1) each of the subgraphs S in G are compressed (i.e., replaced by a nonterminal) in the (unique) initial graph I , and (2) the set of generated terminal graphs is the singleton {G}.acceptance rate: 39%status: publishe

Spatially Aware Computing for Natural Interaction

Spatial information refers to the location of an object in a physical or digital world. Besides, it also includes the relative position of an object related to other objects around it. In this dissertation, three systems are designed and developed. All of them apply spatial information in different fields. The ultimate goal is to increase the user friendliness and efficiency in those applications by utilizing spatial information. The first system is a novel Web page data extraction application, which takes advantage of 2D spatial information to discover structured records from a Web page. The extracted information is useful to re-organize the layout of a Web page to fit mobile browsing. The second application utilizes the 3D spatial information of a mobile device within a large paper-based workspace to implement interactive paper that combines the merits of paper documents and mobile devices. This application can overlay digital information on top of a paper document based on the location of a mobile device within a workspace. The third application further integrates 3D space information with sound detection to realize an automatic camera management system. This application automatically controls multiple cameras in a conference room, and creates an engaging video by intelligently switching camera shots among meeting participants based on their activities. Evaluations have been made on all three applications, and the results are promising. In summary, this dissertation comprehensively explores the usage of spatial information in various applications to improve the usability

INFERENCE OF EDGE REPLACEMENT GRAPH GRAMMARS

We describe an algorithm and experiments for inference of edge replacement graph grammars. This method generates candidate recursive graph grammar productions based on isomorphic subgraphs which overlap by two nodes. If there is no edge between the two overlapping nodes, the method generates a recursive graph grammar production with a virtual edge. We guide the search for the graph grammar based on the size of the grammar and the portion of the graph described by the grammar. We show experiments where we generate graphs from known graph grammars, use our method to infer the grammar from the generated graphs, and then measure the error between the original and inferred grammars. Experiments show that the method performs well on several types of grammars, and specifically that error decreases with increased numbers of unique labels in the graph