New data structures for orthogonal range queries
SIAM Journal on Computing
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Sublinear time algorithms for metric space problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Distances in benzenoid systems: further developments
Proceedings of the conference on Discrete metric spaces
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Geometric Spanner Networks
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
Discrete & Computational Geometry
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Efficient algorithms for network center/covering location optimization problems
Efficient algorithms for network center/covering location optimization problems
Efficient algorithms for the weighted 2-center problem in a cactus graph
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
On the dilation spectrum of paths, cycles, and trees
Computational Geometry: Theory and Applications
Improved algorithms to network p-center location problems
Computational Geometry: Theory and Applications
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We show that, for any fixed constant k=3, the sum of the distances between all pairs of vertices of an abstract graph with n vertices and treewidth at most k can be computed in O(nlog^k^-^1n) time. We also show that, for any fixed constant k=2, the dilation of a geometric graph (i.e., a graph drawn in the plane with straight-line segments) with n vertices and treewidth at most k can be computed in O(nlog^k^+^1n) expected time. The dilation (or stretch-factor) of a geometric graph is defined as the largest ratio, taken over all pairs of vertices, between the distance measured along the graph and the Euclidean distance. The algorithms for both problems are based on the same principle: data structures for orthogonal range searching in bounded dimension provide a compact representation of distances in abstract graphs of bounded treewidth.