The role of twins in computing planar supports of hypergraphs

A support or realization of a hypergraph $H$ is a graph $G$ on the same vertex as $H$ such that for each hyperedge of $H$ it holds that its vertices induce a connected subgraph of $G$. The NP-hard problem of finding a planar} support has applications in hypergraph drawing and network design. Previous algorithms for the problem assume that twins}---pairs of vertices that are in precisely the same hyperedges---can safely be removed from the input hypergraph. We prove that this assumption is generally wrong, yet that the number of twins necessary for a hypergraph to have a planar support only depends on its number of hyperedges. We give an explicit upper bound on the number of twins necessary for a hypergraph with $m$ hyperedges to have an $r$-outerplanar support, which depends only on $r$ and $m$. Since all additional twins can be safely removed, we obtain a linear-time algorithm for computing $r$-outerplanar supports for hypergraphs with $m$ hyperedges if $m$ and $r$ are constant; in other words, the problem is fixed-parameter linear-time solvable with respect to the parameters $m$ and $r$

Annual Report 2016-2017

The College of Computing and Digital Media has always prided itself on curriculum, creative work, and research that stays current with changes in our various fields of instruction. As we looked back on our 2016-17 academic year, the need to chronicle the breadth and excellence of this work became clear. We are pleased to share with you this annual report, our first, highlighting our accomplishments. Last year, we began offering three new graduate programs and two new certificate programs. We also planned six degree programs and three new certificate programs for implementation in the current academic year. CDM faculty were published more than 100 times, had their films screened more than 200 times, and participated in over two dozen exhibitions. Our students were recognized for their scholarly and creative work, and our alumni accomplished amazing things, from winning a Student Academy Award to receiving a Pulitzer. We are proud of all the work we have done together. One notable priority for us in 2016-17 was creating and strengthening relationships with industry—including expanding our footprint at Cinespace and developing the iD Lab—as well as with the community, through partnerships with the Chicago Housing Authority, Wabash Lights, and other nonprofit organizations. We look forward to continuing to provide innovative programs and spaces this academic year. Two areas in particular we’ve been watching closely are makerspaces and the “internet of things.” We’ve already made significant commitments to these areas through the creation of our 4,500 square foot makerspace, the Idea Realization Lab, and our new cyber-physical systems bachelor’s program and lab. We are excited to continue providing the opportunities, curriculum, and facilities to support our remarkable students. David MillerDean, College of Computing and Digital Mediahttps://via.library.depaul.edu/cdmannual/1000/thumbnail.jp

Twins in Subdivision Drawings of Hypergraphs

Visualizing hypergraphs, systems of subsets of some universe, has continuously attracted research interest in the last decades. We study a natural kind of hypergraph visualization called subdivision drawings. Dinkla et al. [Comput. Graph. Forum ’12] claimed that only few hypergraphs have a subdivision drawing. However, this statement seems to be based on the assumption (also used in previous work) that the input hypergraph does not contain twins, pairs of vertices which are in precisely the same hyperedges (subsets of the universe). We show that such vertices may be necessary for a hypergraph to admit a subdivision drawing. As a counterpart, we show that the number of such “necessary twins” is upper-bounded by a function of the number m of hyperedges and a further parameter r of the desired drawing related to its number of layers. This leads to a linear-time algorithm for determining such subdivision drawings if m and r are constant; in other words, the problem is linear-time fixed-parameter tractable with respect to the parameters m and r