TY - GEN
T1 - Fast pruning of geometric spanners
AU - Gudmundsson, J.
AU - Narasimhan, G.
AU - Smid, M.H.M.
PY - 2005
Y1 - 2005
N2 - Let S be a set of points in R d . Given a geometric spanner graph, G = (S,E), with constant stretch factor t, and a positive constant e, we show how to construct a (1+e)-spanner of G with O(|S|) edges in time O(|E|+|S|log|S|) . Previous algorithms require a preliminary step in which the edges are sorted in non-decreasing order of their lengths and, thus, have running time O(|E| log |S|). We obtain our result by designing a new algorithm that finds the pair in a well-separated pair decomposition separating two given query points. Previously, it was known how to answer such a query in O(log|S|) time. We show how a sequence of such queries can be answered in O(1) amortized time per query, provided all query pairs are from a polynomially bounded range.
AB - Let S be a set of points in R d . Given a geometric spanner graph, G = (S,E), with constant stretch factor t, and a positive constant e, we show how to construct a (1+e)-spanner of G with O(|S|) edges in time O(|E|+|S|log|S|) . Previous algorithms require a preliminary step in which the edges are sorted in non-decreasing order of their lengths and, thus, have running time O(|E| log |S|). We obtain our result by designing a new algorithm that finds the pair in a well-separated pair decomposition separating two given query points. Previously, it was known how to answer such a query in O(log|S|) time. We show how a sequence of such queries can be answered in O(1) amortized time per query, provided all query pairs are from a polynomially bounded range.
U2 - 10.1007/978-3-540-31856-9_42
DO - 10.1007/978-3-540-31856-9_42
M3 - Conference contribution
SN - 3-540-24998-2
T3 - Lecture Notes in Computer Science
SP - 508
EP - 520
BT - STACS 2005 (Proceedings 22nd Annual Symposium on Theoretical Aspects of Computer Science, Stuttgart, Germany, February 24-26, 2005)
A2 - Diekert, V.
A2 - Durand, B.
PB - Springer
CY - Berlin
ER -