#### Filter Results:

#### Publication Year

1977

2013

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

We show that if a sequence s/ of natural numbers has no pair of elements whose difference is a positive square, then the density of J / n{l,...,«} is O(l/log«) c »), c n->-oo. This improves previous results which showed that the density converges to zero, but at a slower rate. We use a technique based on the method of Hardy and Littlewood together with a… (More)

- Richard Cole, Jeffrey S. Salowe, William L. Steiger, Endre Szemerédi
- SIAM J. Comput.
- 1989

- Jeffrey S. Salowe, William L. Steiger
- J. Algorithms
- 1987

- Chi-Yuan Lo, Jirí Matousek, William L. Steiger
- Discrete & Computational Geometry
- 1993

Given disjoint sets PI, P2 ..... Pd in R a with n points in total, a ham-sandwich cut is a hyperplane that simultaneously bisects the Pi. We present algorithms for finding ham-sandwich cuts in every dimension d > 1. When d = 2, the algorithm is optimal, having complexity O(n). For dimension d > 2, the bound on the running time is proportional to the… (More)

- J. Michael Steele, William L. Steiger
- Discrete Applied Mathematics
- 1986

- Adrian Dumitrescu, William L. Steiger
- Discrete Mathematics
- 2000

Let Ë be a set with Ò Û · points in general position in the plane, Û of them white, and of them black, where Û and are even numbers. We show that there exists a matching of points of the same color with straight line segments and no crossings which matches at least ¿¿¿± of the points. We also derive an Ç´Ò ÐÓÓ Òµ algorithm which achieves this guarantee. On… (More)

- Prabhakar Ragde, William L. Steiger, Endre Szemerédi, Avi Wigderson
- SIAM J. Discrete Math.
- 1988

We consider the problem of element distinctness. Here $n$ synchronized processors, each given an integer input, must decide whether these integers are pairwise distinct, while communicating via an infinitely large shared memory. If simultaneous write access to a memory cell is forbidden, then a lower bound of $\Omega(log n)$ on the number of steps easily… (More)

- William L. Steiger, Ileana Streinu
- Comput. Geom.
- 1998

We consider three problems about the illumination of planar regions with oodlights of prescribed angles. Problem 1 is the decision problem: given a wedge W of angle , n points p 1 ; ; p n in the plane and n angles 1 ; ; n summing up to , decide whether W can be illuminated by oodlights of angles 1 ; ; n placed in some order at the points p 1 ; ; p n and… (More)

- János Pach, William L. Steiger, Endre Szemerédi
- FOCS
- 1989

- Stefan Langerman, William L. Steiger
- STACS
- 2003

Many problems can be formulated as the optimization of functions in R 2 which are implicitly defined by an arrangement of lines, halfplanes, or points, for example linear programming in the plane. We present an efficient general approach to find the optimum exactly, for a wide range of functions that possess certain useful properties. To illustrate the… (More)