Computational geometry: an introduction
Computational geometry: an introduction
Planar point location using persistent search trees
Communications of the ACM
Shortest paths in Euclidean graphs
Algorithmica
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Journal of Algorithms
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Ray shooting in polygons using Geodesic triangulations
Proceedings of the 18th international colloquium on Automata, languages and programming
Dynamic ray shooting and shortest paths via balanced geodesic triangulations
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Combinatorial aspects of geometric graphs
Computational Geometry: Theory and Applications
Dynamic Trees and Dynamic Point Location
SIAM Journal on Computing
A new point-location algorithm and its practical efficiency: comparison with existing algorithms
ACM Transactions on Graphics (TOG)
Communications of the ACM
Shortest Path Algorithms: An Evaluation Using Real Road Networks
Transportation Science
Computing the shortest path: A search meets graph theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Combining speed-up techniques for shortest-path computations
Journal of Experimental Algorithmics (JEA)
Studying (non-planar) road networks through an algorithmic lens
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Linear-time algorithms for geometric graphs with sublinearly many crossings
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Highway hierarchies hasten exact shortest path queries
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Tracking moving objects with few handovers
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Multi-agent system for parallel road network hierarchization
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part II
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A geometric graph is a graph embedded in the plane with vertices at points and edges drawn as curves (which are usually straight line segments) between those points. The average transversal complexity of a geometric graph is the number of edges of that graph that are crossed by random line or line segment. In this paper, we study the average transversal complexity of road networks. By viewing road networks as multiscale-dispersed graphs, we show that a random line will cross the edges of such a graph O(√n) times on average. In addition, we provide by empirical evidence from experiments on the road networks of the fifty states of United States and the District of Columbia that this bound holds in practice and has a small constant factor. Combining this result with data structuring techniques from computational geometry, allows us to show that we can then do point location and ray-shooting navigational queries with respect to road networks in O(√n log n) expected time. Finally, we provide empirical justification for this claim as well.