AffiliationUniv Arizona, Dept Comp Sci
MetadataShow full item record
CitationDe Luca, F., Hossain, M. I., Kobourov, S., Lubiw, A., & Mondal, D. (2019). Recognition and drawing of stick graphs. Theoretical Computer Science, 796, 22-33.
JournalTHEORETICAL COMPUTER SCIENCE
Rights© 2019 Elsevier B.V. All rights reserved.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractA Stick graph is an intersection graph of axis-aligned segments such that the left endpoints of the horizontal segments and the bottom end-points of the vertical segments lie on a "ground line," a line with slope - 1. It is an open question to decide in polynomial time whether a given bipartite graph G with bipartition A boolean OR B has a Stick representation where the vertices in A and B correspond to horizontal and vertical segments, respectively. We prove that G has a Stick representation if and only if there are orderings of A and B such that G's bipartite adjacency matrix with rows A and columns B excludes three small 'forbidden' submatrices. This is similar to characterizations for other classes of bipartite intersection graphs. We present an algorithm to test whether given orderings of A and B permit a Stick representation respecting those orderings, and to find such a representation if it exists. The algorithm runs in time linear in the size of the adjacency matrix. For the case when only the ordering of A is given, or neither ordering is given, we present some partial results about graphs that are, or are not, Stick representable. (C) 2019 Elsevier B.V. All rights reserved.
Note24 month embargo; available online 19 August 2019.
VersionFinal accepted manuscript
SponsorsNatural Sciences and Engineering Research Council of Canada (NSERC); National Science Foundation (NSF) [CCF-1740858, CCF-1712119, DMS-1839274, DMS-1839307]
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SAME STATS, DIFFERENT GRAPHS (GRAPH STATISTICS AND WHY WE NEED GRAPH DRAWING)Kobourov, Stephen; Chen, Hang (The University of Arizona., 2018)Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe’s Quartet demonstrates how such statistics can be misleading. We consider a similar problem in the context of graph mining. To study the relationships between different graph properties and statistics, we examine all low-order ( 10) non-isomorphic graphs and provide a simple visual analytics system to explore correlations across multiple graph properties. However, for graphs with more than ten nodes, generating the entire space of graphs becomes quickly intractable. We use different random graph generation methods to further look into the distribution of graph statistics for higher order graphs and investigate the impact of various sampling methodologies. We also describe a method for generating many graphs that are identical over a number of graph properties and statistics yet are clearly different and identifiably distinct.
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