TY - GEN
T1 - A Fast Algorithm for Computing a Planar Support for Non-Piercing Rectangles
AU - Pal, Ambar
AU - Raman, Rajiv
AU - Ray, Saurabh
AU - Singh, Karamjeet
N1 - Publisher Copyright:
© Ambar Pal, Rajiv Raman, Saurabh Ray, and Karamjeet Singh.
PY - 2024/12/4
Y1 - 2024/12/4
N2 - For a hypergraph H = (X, έ) a support is a graph G on X such that for each E ∈ έ, the induced subgraph of G on the elements in E is connected. If G is planar, we call it a planar support. A set of axis parallel rectangles R forms a non-piercing family if for any R1, R2 ∈ R, R1 \ R2 is connected. Given a set P of n points in R2 and a set R of m non-piercing axis-aligned rectangles, we give an algorithm for computing a planar support for the hypergraph (P, R) in O(n log2 n + (n + m) log m) time, where each R ∈ R defines a hyperedge consisting of all points of P contained in R.
AB - For a hypergraph H = (X, έ) a support is a graph G on X such that for each E ∈ έ, the induced subgraph of G on the elements in E is connected. If G is planar, we call it a planar support. A set of axis parallel rectangles R forms a non-piercing family if for any R1, R2 ∈ R, R1 \ R2 is connected. Given a set P of n points in R2 and a set R of m non-piercing axis-aligned rectangles, we give an algorithm for computing a planar support for the hypergraph (P, R) in O(n log2 n + (n + m) log m) time, where each R ∈ R defines a hyperedge consisting of all points of P contained in R.
KW - Algorithms
KW - Computational Geometry
KW - Hypergraphs
KW - Visualization
UR - https://www.scopus.com/pages/publications/85213005041
U2 - 10.4230/LIPIcs.ISAAC.2024.53
DO - 10.4230/LIPIcs.ISAAC.2024.53
M3 - Conference contribution
AN - SCOPUS:85213005041
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 35th International Symposium on Algorithms and Computation, ISAAC 2024
A2 - Mestre, Julian
A2 - Wirth, Anthony
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 35th International Symposium on Algorithms and Computation, ISAAC 2024
Y2 - 8 December 2024 through 11 December 2024
ER -