论文信息 - Lower bounds for maximal and convex layers problems

Lower bounds for maximal and convex layers problems

In this paper we derive tight lower bounds for the maximal and convex layers problems in the plane. Our lower bound proofs for the maxima problem and convex hull problem are simpler than those previously known. We also obtain an Ω(nlog n) lower bound for the maximal depth problem, and the convex depth problem, when the points are given in sorted order of their x-coordinates.

Sanjiv Kapoor | Prakash V. Ramanan

[1] F. P. Preparata,et al. Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[2] Prakash V. Ramanan. Obtaining Lower Bounds Using Artificial Components , 1987, Inf. Process. Lett..

[3] David G. Kirkpatrick,et al. Output-size sensitive algorithms for finding maximal vectors , 1985, SCG '85.

[4] David G. Kirkpatrick,et al. The Ultimate Planar Convex Hull Algorithm? , 1986, SIAM J. Comput..

[5] Franco P. Preparata,et al. An optimal real-time algorithm for planar convex hulls , 1979, CACM.

[6] Andrew Chi-Chih Yao,et al. A Lower Bound to Finding Convex Hulls , 1981, JACM.

[7] Peter van Emde Boas,et al. On the Omega(n log n) Lower Bound for Convex Hull and Maximal Vector Determination , 1980, Inf. Process. Lett..

[8] Ronald L. Graham,et al. An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[9] J. Michael Steele,et al. Lower Bounds for Algebraic Decision Trees , 1982, J. Algorithms.

[10] Alfred V. Aho,et al. The Design and Analysis of Computer Algorithms , 1974 .

[11] Bernard Chazelle. OPTIMAL ALGORITHMS FOR COMPUTING DEPTHS AND LAYERS. , 1983 .

[12] Michael Ben-Or,et al. Lower bounds for algebraic computation trees , 1983, STOC.

[13] Bernard Chazelle,et al. On the convex layers of a planar set , 1985, IEEE Trans. Inf. Theory.