# M. N. Kolountzakis

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- Publications
- Influence

Analysis of probabilistic roadmaps for path planning

- L. Kavraki, M. N. Kolountzakis, J. Latombe
- Computer Science
- Proceedings of IEEE International Conference on…
- 22 April 1996

Provides an analysis of a path planning method which uses probabilistic roadmaps. This method has proven very successful in practice, but the theoretical understanding of its performance is still… Expand

Analysis of probabilistic roadmaps for path planning

- L. Kavraki, M. N. Kolountzakis, J. Latombe
- Computer Science
- IEEE Trans. Robotics Autom.
- 1998

We provide an analysis of a recent path planning method which uses probabilistic roadmaps. This method has proven very successful in practice, but the theoretical understanding of its performance is… Expand

Multiple lattice tiles and Riesz bases of exponentials

- M. N. Kolountzakis
- Mathematics
- 12 May 2013

Suppose $\Omega\subseteq\RR^d$ is a bounded and measurable set and $\Lambda \subseteq \RR^d$ is a lattice. Suppose also that $\Omega$ tiles multiply, at level $k$, when translated at the locations… Expand

Fast Computation of the Euclidian Distance Maps for Binary Images

- M. N. Kolountzakis, Kiriakos N. Kutulakos
- Mathematics, Computer Science
- Inf. Process. Lett.
- 28 September 1992

Abstract A simple algorithm is given for the computation of the Euclidian distance from the set of black points in an N × N black and white image, for all points in the image. The running time is… Expand

On the Structure of Multiple Translational Tilings by Polygonal Regions

- M. N. Kolountzakis
- Mathematics, Computer Science
- Discret. Comput. Geom.
- 14 April 1999

Abstract. We consider polygons with the following ``pairing property'': for each edge of the polygon there is precisely one other edge parallel to it. We study the problem of when such a polygon K… Expand

Tiles with no spectra

- M. N. Kolountzakis, M. Matolcsi
- Mathematics
- 7 June 2004

Abstract We exhibit a subset of a finite Abelian group, which tiles the group by translation, and such that its tiling complements do not have a common spectrum (orthogonal basis for their L 2 space… Expand

Fuglede's conjecture on cyclic groups of order $p^nq$

- Romanos-Diogenes Malikiosis, M. N. Kolountzakis
- Mathematics
- 5 December 2016

Fuglede's conjecture on cyclic groups of order $p^nq$, Discrete Analysis 2017:12, 16 pp.
A conjecture of Fuglede from 1974 states that a measurable set $E\subset \mathbb R^n$ of positive Lebesgue… Expand

Structure of tilings of the line by a function

- M. N. Kolountzakis, J. Lagarias
- Mathematics
- 1 March 1996

A function f 2 L 1 (R) tiles the line with a constant weight w using the discrete tile set A if P a2A f(x ? a) = w almost everywhere. A set A is of bounded density if there is a constant C such that… Expand

The Density ofBh[g] Sequences and the Minimum of Dense Cosine Sums

- M. N. Kolountzakis
- Mathematics
- 1996

A setEof integers is called aBh[g] set if every integer can be written in at mostgdifferent ways as a sum ofhelements ofE. We give an upper bound for the size of aBh[1] subset {n1, …,nk} of {1, …,n}… Expand

On the Steinhaus tiling problem

- M. N. Kolountzakis, T. Wolff
- Mathematics
- 1 December 1999

Several results are proved related to a question of Steinhaus: is there a set E ⊂ℝ 2 such that the image of E under each rigid motion of IR2 contains exactly one lattice point? Assuming… Expand