The problem of finding a collection of curves of minimum total length that meet all the lines intersecting a given planar convex body was initiated by Mazurkiewicz in 1916. Such a collection forms an opaque barrier for the convex body. In 1991, Sherme . . .

"We revisit the traveling salesman problem with neighborhoods (TSPN) and propose several new approximation algorithms. These constitute either first approximations (for hyperplanes, lines, and balls in Rd, for d ⩾ 3) or improvements over previous appr . . .

For points p1,…,pn in the unit square [0,1]2, an anchored rectangle packing consists of interior-disjoint axis-aligned empty rectangles r1,…,rn⊆[0,1]2 such that point pi is a corner of the rectangle ri (that is, ri is anchored at pi) for i=1,…,n. We s . . .

We show that the maximum number of convex polygons in a triangulation of n points in the plane is O(1.5029 n ). This improves an earlier bound of O(1.6181 n ) established by van Kreveld, Löffler and Pach (2012), and almost matches the current best low . . .

We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, nonweighted common geometric graphs drawn on $n$ points in the plane in general position (with no three points collinear): perfect matchings, spannin . . .

We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of $n$ points in the plane. Configurations of interest include \emph{convex polygons}, \emph{star-s . . .

For two planar convex bodies, C and D , consider a packing S of n positive homothets of C contained in D . We estimate the total perimeter of the bodies in S , denoted per(S) , in terms of per(D) and n . When all homothets of C touch the boundary of t . . .

For points in the unit square , an anchored rectangle packing consists of interior-disjoint axis-aligned empty rectangles such that point is a corner of the rectangle (that is, is anchored at ) for . We show that for every set of points in , there is . . .

Let S be a set of n points in the unit square [,1]2, one of which is the origin. We construct n pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in S, and the rectangles jointly cove . . .

Given n points in the plane, a covering path is a polygonal path that visits all the points. If no three points are collinear, every covering path requires at least n/2 segments, and n−1 straight line segments obviously suffice even if the covering pa . . .