Cost-sensitive analysis of communication protocols
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Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
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STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A network-flow technique for finding low-weight bounded-degree spanning trees
Journal of Algorithms
Bicriteria network design problems
Journal of Algorithms
Balancing minimum spanning and shortest path trees
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Approximating the weight of shallow Steiner trees
Discrete Applied Mathematics
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Steiner points in tree metrics don't (really) help
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A constant factor approximation for the single sink edge installation problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Simultaneous optimization for concave costs: single sink aggregation or single source buy-at-bulk
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Performance-Driven Global Routing for Cell Based ICs
ICCD '91 Proceedings of the 1991 IEEE International Conference on Computer Design on VLSI in Computer & Processors
New Results of Fault Tolerant Geometric Spanners
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Distributed Maintenance of Resource Efficient Wireless Network Topologies (Distinguished Paper)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry CCCG02
Euclidean Bounded-Degree Spanning Tree Ratios
Discrete & Computational Geometry
Universal approximations for TSP, Steiner tree, and set cover
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Geometric Spanner Networks
Well-separated pair decomposition in linear time?
Information Processing Letters
Experimental study of geometric t-spanners: a running time comparison
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Low-Light Trees, and Tight Lower Bounds for Euclidean Spanners
Discrete & Computational Geometry
One Tree Suffices: A Simultaneous O(1)-Approximation for Single-Sink Buy-at-Bulk
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Prim-Dijkstra tradeoffs for improved performance-driven routing tree design
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Approximating k-hop minimum-spanning trees
Operations Research Letters
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We show that for every set $\mathcal{S}$ of $n$ points in the plane and a designated point $rt\in\mathcal{S}$, there exists a tree $T$ that has small maximum degree, depth, and weight. Moreover, for every point $v\in\mathcal{S}$, the distance between $rt$ and $v$ in $T$ is within a factor of $(1+\epsilon)$ close to their Euclidean distance $\|rt,v\|$. We call these trees narrow-shallow-low-light (NSLLTs). We demonstrate that our construction achieves optimal (up to constant factors) tradeoffs between all parameters of NSLLTs. Our construction extends to point sets in $\mathbb{R}^d$ for an arbitrarily large constant $d$. The running time of our construction is $O(n\cdot\log n)$. We also study this problem in general metric spaces, and show that NSLLTs with small maximum degree, depth, and weight can always be constructed if one is willing to compromise the root-distortion. On the other hand, we show that the increased root-distortion is inevitable, even if the point set $\mathcal{S}$ resides in a Euclidean space of dimension $\Theta(\log n)$. In addition, we show that if one is allowed to use Steiner points, then it is possible to achieve root-distortion of $(1+\epsilon)$ together with small maximum degree, depth, and weight for general metric spaces. Finally, we establish some lower bounds on the power of Steiner points in the context of Euclidean spanning trees and spanners.