1,301 research outputs found
On the random greedy F-free hypergraph process
Let be a strictly -balanced -uniform hypergraph with and maximum co-degree at least two. The random greedy -free process
constructs a maximal -free hypergraph as follows. Consider a random ordering
of the hyperedges of the complete -uniform hypergraph on
vertices. Start with the empty hypergraph on vertices. Successively
consider the hyperedges of in the given ordering, and add to
the existing hypergraph provided that does not create a copy of . We
show that asymptotically almost surely this process terminates at a hypergraph
with hyperedges. This is best possible up
to logarithmic factors
Block Crossings in Storyline Visualizations
Storyline visualizations help visualize encounters of the characters in a
story over time. Each character is represented by an x-monotone curve that goes
from left to right. A meeting is represented by having the characters that
participate in the meeting run close together for some time. In order to keep
the visual complexity low, rather than just minimizing pairwise crossings of
curves, we propose to count block crossings, that is, pairs of intersecting
bundles of lines.
Our main results are as follows. We show that minimizing the number of block
crossings is NP-hard, and we develop, for meetings of bounded size, a
constant-factor approximation. We also present two fixed-parameter algorithms
and, for meetings of size 2, a greedy heuristic that we evaluate
experimentally.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
- …