TY - GEN
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 - 2015
Y1 - 2015
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 each cell has the same nearest neighbors in S. Classically, both structures can be computed in O(n log 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 a triangulation of S in time O(n2/s + n log n log s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n2/s) log s + n log s log∗ 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 each cell has the same nearest neighbors in S. Classically, both structures can be computed in O(n log 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 a triangulation of S in time O(n2/s + n log n log s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n2/s) log s + n log s log∗ s).
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U2 - 10.1007/978-3-319-21840-3_40
DO - 10.1007/978-3-319-21840-3_40
M3 - Conference contribution
AN - SCOPUS:84951771493
SN - 9783319218397
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 482
EP - 494
BT - Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings
A2 - Dehne, Frank
A2 - Sack, Jorg-Rudiger
A2 - Stege, Ulrike
PB - Springer Verlag
T2 - 14th International Symposium on Algorithms and Data Structures, WADS 2015
Y2 - 5 August 2015 through 7 August 2015
ER -