TY - GEN
T1 - Twins in subdivision drawings of hypergraphs
AU - van Bevern, René
AU - Kanj, Iyad
AU - Komusiewicz, Christian
AU - Niedermeier, Rolf
AU - Sorge, Manuel
N1 - Publisher Copyright:
© Springer International Publishing AG 2016.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85007398584&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-50106-2_6
DO - 10.1007/978-3-319-50106-2_6
M3 - Conference contribution
AN - SCOPUS:85007398584
SN - 9783319501055
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 67
EP - 80
BT - Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers
A2 - Nollenburg, Martin
A2 - Hu, Yifan
PB - Springer Verlag
T2 - 24th International Symposium on Graph Drawing and Network Visualization, GD 2016
Y2 - 19 September 2016 through 21 September 2016
ER -