A heuristic triangulation algorithm
Journal of Algorithms
Approximation algorithms for planar traveling salesman tours and minimum-length triangulations
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Quasi-greedy triangulations approximating the minimum weight triangulation
Journal of Algorithms
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Decomposing a polygon into its convex parts
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
A Note on Convex Decompositions of a Set of Points in the Plane
Graphs and Combinatorics
Practical and robust geographic routing in wireless networks
SenSys '04 Proceedings of the 2nd international conference on Embedded networked sensor systems
Competitive online routing in geometric graphs
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
On a conjecture related to geometric routing
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
A quasi-polynomial time approximation scheme for minimum weight triangulation
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Minimum weight triangulation is NP-hard
Proceedings of the twenty-second annual symposium on Computational geometry
Geometric Spanner Networks
Light orthogonal networks with constant geometric dilation
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Approximation algorithms for the minimum convex partition problem
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Geometric spanners for routing in mobile networks
IEEE Journal on Selected Areas in Communications
Light orthogonal networks with constant geometric dilation
Journal of Discrete Algorithms
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New tight bounds are presented on the minimum length of planar straight line graphs connecting n given points in the plane and having convex faces. Specifically, we show that the convex Steiner partition of n points in the plane is at most O(log n/log log n) times longer than their Euclidean minimum spanning tree (EMST), and this bound is best possible. Without allowing Steiner points, the corresponding bound is known to be Θ(log n), attained for n points lying along a pseudo-triangle. We also show that the convex Steiner partition of n points along a pseudo-triangle is at most O(log log n) times longer than the EMST, and this bound is also best possible. Our methods are constructive and lead to polynomial-time algorithms for computing convex Steiner partitions within these bounds in both cases.