M. Karavelas

activity

20082015

most citedGuarding curvilinear art galleries with edge or mobile guards via 2-dominance of triangulation graphs

4 citations · 9 across the 7 of their papers we have counts for

collaborators

7 papers

cs.CG2015★ 2 cited

A geometric approach for the upper bound theorem for Minkowski sums of convex polytopes

Menelaos I. Karavelas, Eleni Tzanaki

We derive tight expressions for the maximum number of $k$ -faces, $0 \leq k \leq d - 1$ , of the Minkowski sum, $P_{1} + ... + P_{r}$ , of $r$ convex $d$ -polytopes $P_{1}, ..., P_{r}$ in $R^{d}$ …

cs.CG2012

The maximum number of faces of the Minkowski sum of three convex polytopes

Menelaos I. Karavelas, Christos Konaxis, Eleni Tzanaki

We derive tight expressions for the maximum number of $k$ -faces, $0 \leq k \leq d - 1$ , of the Minkowski sum, $P_{1} + P_{2} + P_{3}$ , of three $d$ -dimensional convex polytopes $P_{1}$ , $P_{2}$ and $P…

cs.CG2011★ 3 cited

Tight lower bounds on the number of faces of the Minkowski sum of convex polytopes via the Cayley trick

Menelaos I. Karavelas, Eleni Tzanaki

Consider a set of $r$ convex $d$ -polytopes $P_{1}, P_{2}, ..., P_{r}$ , where $d \geq 3$ and $r \geq 2$ , and let $n_{i}$ be the number of vertices of $P_{i}$ , $1 \leq i \leq r$ . It has been shown by…

cs.CG2011

Analysis of the Incircle predicate for the Euclidean Voronoi diagram of axes-aligned line segments

Manos N. Kamarianakis, Menelaos I. Karavelas

In this paper we study the most-demanding predicate for computing the Euclidean Voronoi diagram of axes-aligned line segments, namely the Incircle predicate. Our contribution is tw…

cs.CG2011

The maximum number of faces of the Minkowski sum of two convex polytopes

Menelaos I. Karavelas, Eleni Tzanaki

We derive tight expressions for the maximum number of $k$ -faces, $0 \leq k \leq d - 1$ , of the Minkowski sum, $P_{1} \oplus P_{2}$ , of two $d$ -dimensional convex polytopes $P_{1}$ and $P_{2}$ ,…

cs.CG2009

Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes

Menelaos I. Karavelas, Eleni Tzanaki

Given a set $Σ$ of spheres in $E^{d}$ , with $d \geq 3$ and $d$ odd, having a fixed number of $m$ distinct radii $ρ_{1}, ρ_{2}, ..., ρ_{m}$ , we show that the worst-case combinatorial c…

cs.CG2008★ 4 cited

Guarding curvilinear art galleries with edge or mobile guards via 2-dominance of triangulation graphs

Menelaos I. Karavelas

We consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves, with edge or mobile guards. Our focus is on piecewise-convex polyg…