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Approximating k-Hop Minimum-Spanning Trees

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44003

Althaus,  Ernst
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44464

Funke,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44808

Könemann,  Jochen
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45255

Ramos,  Edgar A.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45503

Skutella,  Martin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Althaus, E., Funke, S., Har-Peled, S., Könemann, J., Ramos, E. A., & Skutella, M. (2005). Approximating k-Hop Minimum-Spanning Trees. Operations Research Letters, 33, 115-120.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-25C1-0
Abstract
In this paper we consider the problem of computing minimum-cost spanning trees with depth restrictions. Specifically, we are given an $n$-node complete graph $G$, a metric cost-function $c$ on its edges, and an integer $k\geq 1$. The goal in the minimum-cost $k$-hop spanning tree problem is to compute a spanning tree $T$ in $G$ of minimum total cost such that the longest root-leaf-path in the tree has at most $k$ edges. Our main result is an algorithm that computes a tree of depth at most $k$ and total expected cost $O(\log n)$ times that of a minimum-cost $k$-hop spanning-tree. The result is based upon earlier work on metric space approximation due to Fakcharoenphol et al.[FRT03] and Bartal [Bart96,Bart98]. In particular we show that the problem can be solved exactly in polynomial time when the cost metric $c$ is induced by a so-called hierarchically well-separated tree.