10 research outputs found
On Upward Drawings of Trees on a Given Grid
Computing a minimum-area planar straight-line drawing of a graph is known to
be NP-hard for planar graphs, even when restricted to outerplanar graphs.
However, the complexity question is open for trees. Only a few hardness results
are known for straight-line drawings of trees under various restrictions such
as edge length or slope constraints. On the other hand, there exist
polynomial-time algorithms for computing minimum-width (resp., minimum-height)
upward drawings of trees, where the height (resp., width) is unbounded.
In this paper we take a major step in understanding the complexity of the
area minimization problem for strictly-upward drawings of trees, which is one
of the most common styles for drawing rooted trees. We prove that given a
rooted tree and a grid, it is NP-hard to decide whether
admits a strictly-upward (unordered) drawing in the given grid.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Analysis of road network pattern considering population distribution and central business district.
This paper proposes a road network growing model with the consideration of population distribution and central business district (CBD) attraction. In the model, the relative neighborhood graph (RNG) is introduced as the connection mechanism to capture the haracteristics of road network topology. The simulation experiment is set up to illustrate the effects of population distribution and CBD attraction on the characteristics of road network. Moreover, several topological attributes of road network is evaluated by using coverage, circuitness, treeness and total length in the experiment. Finally, the suggested model is verified in the simulation of China and Beijing Highway networks