Computing a ham-sandwich cut in two dimensions
Journal of Symbolic Computation
Edge-skeletons in arrangements with applications
Algorithmica
On k-hulls and related problems
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Sorting in c log n parallel steps
Combinatorica
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Points and triangles in the plane and halving planes in space
Discrete & Computational Geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Generalizing ham sandwich cuts to equitable subdivisions
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On the Complexity of the Pancake Problem
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 0.00 |
Lo and Steiger resolved the complexity question for computing a planar ham-sandwich cut by giving an optimal linear-time algorithm. We show how to generalize the ideas to every fixed dimension d 2 by describing an algorithm that computes a ham-sandwich cut in Rd in time O(nd–1–a(d)), for some a(d) 0 (going to zero as d increases). For d = 3,4, the running time is almost proportional to ed–1(n;n/2), where dd(k;n) denotes the maximal number of k-sets over sets of n points in Rd, and with the current best bounds, we get O(n3/2 log2 n/log n) running time for d = 3 and O(n8/3+&egr;) for d=4. We also give a linear time algorithm for three dimensional ham-sandwich cuts when the three sets are suitably separated.