TY - GEN

T1 - Shallow-low-light trees, and tight lower bounds for euclidean spanners

AU - Dinitz, Yefim

AU - Elkin, Michael

AU - Solomon, Shay

PY - 2008/12/31

Y1 - 2008/12/31

N2 - We show that for every n-point metric space M and positive integer k, there exists a spanning tree T with unweighted diameter O(k) and weight w(T) = O(k · n1/k) · w(MST(M)), and a spanning tree T′ with weight w(T′) = O(k) · w(MST(M)) and unweighted diameter O(k · n1/k). Moreover, there is a designated point rt such that for every other point v, both distT(rt, v) and distT(rt,v) are at most (1 + ε) · distM(rt,v), for an arbitrarily small constant ε > O. We prove that the above tradeoffs are tight up to constant factors in the entire range of parameters. Furthermore, our lower bounds apply to a basic one-dimensional Euclidean space. Finally, our lower bounds for the particular case of unweighted diameter O(log n) settle a long-standing open problem in Computational Geometry.

AB - We show that for every n-point metric space M and positive integer k, there exists a spanning tree T with unweighted diameter O(k) and weight w(T) = O(k · n1/k) · w(MST(M)), and a spanning tree T′ with weight w(T′) = O(k) · w(MST(M)) and unweighted diameter O(k · n1/k). Moreover, there is a designated point rt such that for every other point v, both distT(rt, v) and distT(rt,v) are at most (1 + ε) · distM(rt,v), for an arbitrarily small constant ε > O. We prove that the above tradeoffs are tight up to constant factors in the entire range of parameters. Furthermore, our lower bounds apply to a basic one-dimensional Euclidean space. Finally, our lower bounds for the particular case of unweighted diameter O(log n) settle a long-standing open problem in Computational Geometry.

UR - http://www.scopus.com/inward/record.url?scp=58049085540&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2008.24

DO - 10.1109/FOCS.2008.24

M3 - Conference contribution

AN - SCOPUS:58049085540

SN - 9780769534367

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 519

EP - 528

BT - Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008

T2 - 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008

Y2 - 25 October 2008 through 28 October 2008

ER -