On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
The complexity and construction of many faces in arrangements of lines and of segments
Discrete & Computational Geometry - Special issue on the complexity of arrangements
Fat triangles determine linearly many holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficient hidden surface removal for objects with small union size
Computational Geometry: Theory and Applications
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On fat partitioning, fat covering and the union size of polygons
Computational Geometry: Theory and Applications
On the union of k-curved objects
Computational Geometry: Theory and Applications
On the Boundary Complexity of the Union of Fat Triangles
SIAM Journal on Computing
Algorithms for Polytope Covering and Approximation
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
The Complexity of the Union of $(\alpha,\beta)$-Covered Objects
SIAM Journal on Computing
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
Improved Bounds on the Union Complexity of Fat Objects
Discrete & Computational Geometry
On the Union of Cylinders in Three Dimensions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Epsilon nets and union complexity
Proceedings of the twenty-fifth annual symposium on Computational geometry
On the union of fat tetrahedra in three dimensions
Journal of the ACM (JACM)
Hitting sets when the VC-dimension is small
Information Processing Letters
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
Better bounds on the union complexity of locally fat objects
Proceedings of the twenty-sixth annual symposium on Computational geometry
Small-Size $\eps$-Nets for Axis-Parallel Rectangles and Boxes
SIAM Journal on Computing
On the structure and composition of forbidden sequences, with geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
Tight lower bounds for the size of epsilon-nets
Proceedings of the twenty-seventh annual symposium on Computational geometry
Semialgebraic Range Reporting and Emptiness Searching with Applications
SIAM Journal on Computing
Weighted capacitated, priority, and geometric set cover via improved quasi-uniform sampling
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Geometric packing under non-uniform constraints
Proceedings of the twenty-eighth annual symposium on Computational geometry
The union of colorful simplices spanned by a colored point set
Computational Geometry: Theory and Applications
Small-size relative (p,ε)-approximations for well-behaved range spaces
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We show that, for any fixed δ 0, the combinatorial complexity of the union of n triangles in the plane, each of whose angles is at least δ, is O(n2α(n) log* n), with the constant of proportionality depending on δ. This considerably improves the twenty-year-old bound O(n log log n), due to Matoušek et al. [24, 25].