TY - JOUR
T1 - Time-space trade-offs for triangulations and Voronoi diagrams
AU - Korman, Matias
AU - Mulzer, Wolfgang
AU - van Renssen, André
AU - Roeloffzen, Marcel
AU - Seiferth, Paul
AU - Stein, Yannik
PY - 2018/8/1
Y1 - 2018/8/1
N2 - Let S be a planar n-point set. A triangulation for S is a maximal plane straight-line graph with vertex set S. The Voronoi diagram for S is the subdivision of the plane into cells such that all points in a cell have the same nearest neighbor in S. Classically, both structures can be computed in O(nlog n) time and O(n) space. We study the situation when the available workspace is limited: given a parameter s∈(1,...,n), an s-workspace algorithm has read-only access to an input array with the points from S in arbitrary order, and it may use only O(s) additional words of Θ(log n) bits for reading and writing intermediate data. The output should then be written to a write-only structure. We describe a deterministic s-workspace algorithm for computing an arbitrary triangulation of S in time O(n2/s+nlog nlog s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n2/s)log s+nlog slog* s).
AB - Let S be a planar n-point set. A triangulation for S is a maximal plane straight-line graph with vertex set S. The Voronoi diagram for S is the subdivision of the plane into cells such that all points in a cell have the same nearest neighbor in S. Classically, both structures can be computed in O(nlog n) time and O(n) space. We study the situation when the available workspace is limited: given a parameter s∈(1,...,n), an s-workspace algorithm has read-only access to an input array with the points from S in arbitrary order, and it may use only O(s) additional words of Θ(log n) bits for reading and writing intermediate data. The output should then be written to a write-only structure. We describe a deterministic s-workspace algorithm for computing an arbitrary triangulation of S in time O(n2/s+nlog nlog s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n2/s)log s+nlog slog* s).
KW - Randomized algorithm
KW - Time-space trade-off
KW - Triangulation
KW - Voronoi diagram
UR - http://www.scopus.com/inward/record.url?scp=85045399673&partnerID=8YFLogxK
U2 - 10.1016/j.comgeo.2017.01.001
DO - 10.1016/j.comgeo.2017.01.001
M3 - Article
AN - SCOPUS:85045399673
SN - 0925-7721
VL - 73
SP - 35
EP - 45
JO - Computational Geometry
JF - Computational Geometry
ER -