Self-adjusting binary search trees
Journal of the ACM (JACM)
There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Algorithms for VLSI Physical Design Automation
Algorithms for VLSI Physical Design Automation
Handbook of Theoretical Computer Science
Handbook of Theoretical Computer Science
Proximate planar point location
Proceedings of the nineteenth annual symposium on Computational geometry
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We propose a definition of locality for properties of geometric graphs. We measure the local density of graphs using region-counting distances between pairs of vertices, and we use this density to define local properties of classes of graphs. We illustrate locality by introducing the local diameter of geometric graphs: we define it as the upper bound on the size of the shortest path between any pair of vertices, expressed as a function of the density of the graph around these vertices. We determine the local diameter of several well-studied graphs such as @Q-graphs, Ordered @Q-graphs and Skip List Spanners. We also show that various operations, such as path and point queries using geometric graphs as data structures, have complexities which can be expressed as local properties.