The Clarkson-Shor technique revisited and extended

We provide an alternative simpler and more general deriva- tion of the Clarkson-Shor probabilistic technique [4] and use it to obtain in addition several extensions and new combi- natorial bounds.

[1]  E. Szemerédi,et al.  Crossing-Free Subgraphs , 1982 .

[2]  F. Thomas Leighton,et al.  Complexity Issues in VLSI , 1983 .

[3]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[4]  Kenneth L. Clarkson,et al.  Applications of random sampling in computational geometry, II , 1988, SCG '88.

[5]  Herbert Edelsbrunner,et al.  Counting triangle crossings and halving planes , 1993, SCG '93.

[6]  Micha Sharir,et al.  Davenport-Schinzel sequences and their geometric applications , 1995, Handbook of Computational Geometry.

[7]  János Pach,et al.  Combinatorial Geometry , 2012 .

[8]  János Pach,et al.  Extremal Problems for Geometric Hypergraphs , 1996, ISAAC.

[9]  Ketan Mulmuley,et al.  Randomized algorithms , 1997 .

[10]  László A. Székely,et al.  Crossing Numbers and Hard Erdős Problems in Discrete Geometry , 1997, Combinatorics, Probability and Computing.

[11]  Martin Aigner,et al.  Proofs from THE BOOK , 1998 .

[12]  Micha Sharir,et al.  An Improved Bound for k-Sets in Three Dimensions , 2000, SCG '00.

[13]  Boris Aronov,et al.  Polytopes in Arrangements , 2001, Discret. Comput. Geom..