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  • Work
    Article
    Gerbner, Dániel
    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 . . .
  • Work
    Article
    Dumitrescu, Adrian
    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 . . .
  • Work
    Article
    Dumitrescu, Adrian
    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 . . .
  • Work
    Article
    Dumitrescu, Adrian
    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 . . .
  • Work
    Article
    Löffler, Maarten
    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 . . .
  • Work
    Article
    Schulz, André
    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 . . .
  • Work
    Article
    Dumitrescu, Adrian
    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 . . .
  • Work
    Article
    Dumitrescu, Adrian
    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 . . .
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    Article
    Dumitrescu, Adrian
    "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 . . .
  • Work
    Article
    Dumitrescu, Adrian
    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 . . .