TY - GEN
T1 - Crossing Patterns in Nonplanar Road Networks
AU - Eppstein, David
AU - Gupta, Siddharth
N1 - Publisher Copyright:
© 2017 Copyright held by the owner/author(s).
PY - 2017/11/7
Y1 - 2017/11/7
N2 - We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross each other. In this paper, we study the sparsity properties of crossing graphs of real-world road networks. We show that, in large road networks (the Urban Road Network Dataset), the crossing graphs have connected components that are primarily trees, and that the remaining non-tree components are typically sparse (technically, that they have bounded degeneracy). We prove theoretically that when an embedded graph has a sparse crossing graph, it has other desirable properties that lead to fast algorithms for shortest paths and other algorithms important in geographic information systems. Notably, these graphs have polynomial expansion, meaning that they and all their subgraphs have small separators.
AB - We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross each other. In this paper, we study the sparsity properties of crossing graphs of real-world road networks. We show that, in large road networks (the Urban Road Network Dataset), the crossing graphs have connected components that are primarily trees, and that the remaining non-tree components are typically sparse (technically, that they have bounded degeneracy). We prove theoretically that when an embedded graph has a sparse crossing graph, it has other desirable properties that lead to fast algorithms for shortest paths and other algorithms important in geographic information systems. Notably, these graphs have polynomial expansion, meaning that they and all their subgraphs have small separators.
KW - Crossings
KW - Nonplanar graphs
KW - Road network
KW - Sparsity
UR - http://www.scopus.com/inward/record.url?scp=85040991346&partnerID=8YFLogxK
U2 - 10.1145/3139958.3139999
DO - 10.1145/3139958.3139999
M3 - Conference contribution
AN - SCOPUS:85040991346
SN - 9781450354905
T3 - GIS: Proceedings of the ACM International Symposium on Advances in Geographic Information Systems
BT - GIS
A2 - Ravada, Siva
A2 - Hoel, Erik
A2 - Tamassia, Roberto
A2 - Newsam, Shawn
A2 - Trajcevski, Goce
A2 - Trajcevski, Goce
PB - Association for Computing Machinery
T2 - 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, ACM SIGSPATIAL GIS 2017
Y2 - 7 November 2017 through 10 November 2017
ER -
