TY - GEN
T1 - Self-approaching graphs
AU - Alamdari, Soroush
AU - Chan, Timothy M.
AU - Grant, Elyot
AU - Lubiw, Anna
AU - Pathak, Vinayak
PY - 2013
Y1 - 2013
N2 - In this paper we introduce self-approaching graph drawings. A straight-line drawing of a graph is self-approaching if, for any origin vertex s and any destination vertex t, there is an st-path in the graph such that, for any point q on the path, as a point p moves continuously along the path from the origin to q, the Euclidean distance from p to q is always decreasing. This is a more stringent condition than a greedy drawing (where only the distance between vertices on the path and the destination vertex must decrease), and guarantees that the drawing is a 5.33-spanner. We study three topics: (1) recognizing self-approaching drawings; (2) constructing self-approaching drawings of a given graph; (3) constructing a self-approaching Steiner network connecting a given set of points. We show that: (1) there are efficient algorithms to test if a polygonal path is self-approaching in ℝ2 and ℝ3, but it is NP-hard to test if a given graph drawing in ℝ3 has a self-approaching uv-path; (2) we can characterize the trees that have self-approaching drawings; (3) for any given set of terminal points in the plane, we can find a linear sized network that has a self-approaching path between any ordered pair of terminals.
AB - In this paper we introduce self-approaching graph drawings. A straight-line drawing of a graph is self-approaching if, for any origin vertex s and any destination vertex t, there is an st-path in the graph such that, for any point q on the path, as a point p moves continuously along the path from the origin to q, the Euclidean distance from p to q is always decreasing. This is a more stringent condition than a greedy drawing (where only the distance between vertices on the path and the destination vertex must decrease), and guarantees that the drawing is a 5.33-spanner. We study three topics: (1) recognizing self-approaching drawings; (2) constructing self-approaching drawings of a given graph; (3) constructing a self-approaching Steiner network connecting a given set of points. We show that: (1) there are efficient algorithms to test if a polygonal path is self-approaching in ℝ2 and ℝ3, but it is NP-hard to test if a given graph drawing in ℝ3 has a self-approaching uv-path; (2) we can characterize the trees that have self-approaching drawings; (3) for any given set of terminal points in the plane, we can find a linear sized network that has a self-approaching path between any ordered pair of terminals.
KW - graph drawing
KW - increasing-chord
KW - self-approaching
UR - http://www.scopus.com/inward/record.url?scp=84874173553&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874173553&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-36763-2_23
DO - 10.1007/978-3-642-36763-2_23
M3 - Conference contribution
AN - SCOPUS:84874173553
SN - 9783642367625
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 260
EP - 271
BT - Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers
T2 - 20th International Symposium on Graph Drawing, GD 2012
Y2 - 19 September 2012 through 21 September 2012
ER -