Discrete Mathematics - Topics on domination
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
Points, spheres, and separators: a unified geometric approach to graph partitioning
Points, spheres, and separators: a unified geometric approach to graph partitioning
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
Dealing with higher dimensions: the well-separated pair decomposition and its applications
Dealing with higher dimensions: the well-separated pair decomposition and its applications
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Kinetic connectivity of rectangles
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Simplified kinetic connectivity for rectangles and hypercubes
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
On Representations of Some Thickness-Two Graphs
GD '95 Proceedings of the Symposium on Graph Drawing
Separating Thickness from Geometric Thickness
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Minimum Spanning Trees in d Dimensions
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
A Deterministic Linear Time Algorithm For Geometric Separators And Its Applications
Fundamenta Informaticae
Edges and switches, tunnels and bridges
Computational Geometry: Theory and Applications
Choosing colors for geometric graphs via color space embeddings
GD'06 Proceedings of the 14th international conference on Graph drawing
K-partite RNA secondary structures
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
Edges and switches, tunnels and bridges
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Spanners for geometric intersection graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We show how to test the bipartiteness of an intersection graph of n line segments or simple polygons in the plane, or of balls in Rd, in time O(n log n). More generally we find subquadratic algorithms for connectivity and bipartiteness testing of intersection graphs of a broad class of geometric objects. For unit balls in Rd, connectivity testing has equivalent randomized complexity to construction of Euclidean minimum spanning trees, and for line segments in the plane connectivity testing has the same lower bounds as Hopcroft's problem; therefore, for these problems, connectivity is unlikely to be solved as efficiently as bipartiteness. For line segments or planar disks, testing k-colorability of intersection graphs for k 2 is NP-complete.