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 -