Fast pruning of geometric spanners

J. Gudmundsson, G. Narasimhan, M.H.M. Smid

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

15 Citaten (Scopus)

Samenvatting

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.
Originele taal-2Engels
TitelSTACS 2005 (Proceedings 22nd Annual Symposium on Theoretical Aspects of Computer Science, Stuttgart, Germany, February 24-26, 2005)
RedacteurenV. Diekert, B. Durand
Plaats van productieBerlin
UitgeverijSpringer
Pagina's508-520
ISBN van geprinte versie3-540-24998-2
DOI's
StatusGepubliceerd - 2005

Publicatie series

NaamLecture Notes in Computer Science
Volume3404
ISSN van geprinte versie0302-9743

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