On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
On the union of fat wedges and separating a collection of segments by a line
Computational Geometry: Theory and Applications
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
The complexity of the free space for a robot moving amidst fat obstacles
Computational Geometry: Theory and Applications
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
On the complexity of the union of fat objects in the plane
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
On the union of κ-curved objects
Proceedings of the fourteenth annual symposium on Computational geometry
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
On the Boundary Complexity of the Union of Fat Triangles
SIAM Journal on Computing
The Complexity of the Union of $(\alpha,\beta)$-Covered Objects
SIAM Journal on Computing
Almost Tight Bound for the Union of Fat Tetrahedra in Three Dimensions
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Improved Bounds on the Union Complexity of Fat Objects
Discrete & Computational Geometry
Small-Size $\eps$-Nets for Axis-Parallel Rectangles and Boxes
SIAM Journal on Computing
Semialgebraic Range Reporting and Emptiness Searching with Applications
SIAM Journal on Computing
Improved bound for the union of fat triangles
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Similarity of polygonal curves in the presence of outliers
Computational Geometry: Theory and Applications
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We prove that the union complexity of a set of n constant-complexity locally fat objects (which can be curved and/or non-convex) in the plane is O(λt+2(n) log n), where t is the maximum number of times the boundaries of any two objects intersect. This improves the previously best known bound by a logarithmic factor.