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- W2005191532 abstract "Consider an edge-weighted tree T = (V, E, w : E r R+), in which a subset R of the nodes (called the required nodes) are colored red and the remaining nodes in S = VR are colored black (and called the Steiner nodes). The shortest-path distance according to the edge-weights defines a metric dT on the vertex set V.We now ask the following question: Is it possible to define another weighted tree T* = (R, E*, w* : E* r R+), this time on just the red vertices so that the shortest-path metric dT* induced by T* on the vertices in R is “close” to the metric dT restricted to the red vertices? I.e., does there exist a weighted tree T* = (R, E*, c*) and a (small) constant a such that dT(u, v) ≤ dT* (u, v) ≤ a dT(u, v) for any two red vertices u, v ∈ R?We answer this question in the affirmative, and give a linear time algorithm to obtain a tree T* with a ≤ 8. We also give two applications of this result: an upper bound, in which we show that emulating multicasts using unicasts can be almost as good as general multicasts for certain performance measures; and a lower bound, in which we give a simple combinatorial proof of the fact that the metric generated by a graph of girthg must suffer a distortion of at least O(g) when approximated by a tree." @default.
- W2005191532 created "2016-06-24" @default.
- W2005191532 creator A5078381067 @default.
- W2005191532 date "2001-01-09" @default.
- W2005191532 modified "2023-09-28" @default.
- W2005191532 title "Steiner points in tree metrics don't (really) help" @default.
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- W2005191532 doi "https://doi.org/10.5555/365411.365448" @default.
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