On k-hulls and related problems
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An improved algorithm for constructing kth-order voronoi diagrams
IEEE Transactions on Computers
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
A fast planar partition algorithm, II
Journal of the ACM (JACM)
On levels in arrangements and Voronoi diagrams
Discrete & Computational Geometry
An upper bound on the number of planar K-sets
Discrete & Computational Geometry
An optimal algorithm for the (≤ k)-levels, with applications to separation and transversal problems
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
On lazy randomized incremental construction
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On geometric optimization with few violated constraints
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications
Proceedings of the eleventh annual symposium on Computational geometry
Efficient searching with linear constraints
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Tight Error Bounds of Geometric Problems on Convex Objects with Imprecise Coordinates
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
| Hi-index | 0.00 |
We give a simple lazy randomized incremental algorithm to compute ≤k-levels in arrangements of x-monotone Jordan curves in the plane, and in arrangements of planes in three-dimensional space. If each pair of curves intersects in at most s points, the expected running time of the algorithm is O(k2&lgr;s(n/k)+min(&lgr;s(n)log2n,k2&lgr;s(n/k)logn)). For the three-dimensional case the expected running time is O(nk2+min(nlog3n,nk2logn)). The algorithm also works for computing the ≤k-level in a set of discs, with an expected running time of O(nk+min(nlog2n,nklogn)). Furthermore, we give a simple algorithm for computing the order-k Voronoi diagram of a set of n points in the plane that runs in expected time O(k(n−k)logn+nlog3n).