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- Lydia E. Kavraki, Mihail N. Kolountzakis, Jean-Claude Latombe
- IEEE Trans. Robotics and Automation
- 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… (More)

- Mihail N. Kolountzakis, Kiriakos N. Kutulakos
- Inf. Process. Lett.
- 1992

- Mihail N. Kolountzakis
- Discrete & Computational Geometry
- 2000

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… (More)

- Mihail N. Kolountzakis, Gary L. Miller, Richard Peng, Charalampos E. Tsourakakis
- Internet Mathematics
- 2012

Suppose Ω ⊆ R is a bounded and measurable set and Λ ⊆ R is a lattice. Suppose also that Ω tiles multiply, at level k, when translated at the locations Λ. This means that the Λ-translates of Ω cover… (More)

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… (More)

- Mihail N. Kolountzakis
- Electr. J. Comb.
- 2003

Suppose that A ⊆ Z is a £nite set of integers of diameter D = max A−min A. Suppose also that B ⊆ Z is such that A ⊕ B = Z, that is each n ∈ Z is uniquely expressible as a + b, a ∈ A, b ∈ B. We say… (More)

- Charalampos E. Tsourakakis, Mihail N. Kolountzakis, Gary L. Miller
- J. Graph Algorithms Appl.
- 2011

In this work, we introduce the notion of triangle sparsifiers, i.e., sparse graphs which are approximately the same to the original graph with respect to the triangle count. This results in a… (More)

- Lydia E. Kavraki, Mihail N. Kolountzakis
- Inf. Process. Lett.
- 1995

Consider the following decision problem. Given a collection of non-overlapping (but possibly touching) polygons in the plane, is there a proper connected subcollection of it that can be separated… (More)

A set E of integers is called a B h g] set if every integer can be written in at most g diierent ways as a sum of h elements of E. We give an upper bound for the size of a B h 1] subset fn 1 ; : : :;… (More)