Matias Korman

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Given a fixed origin <i>o</i> in the <i>d</i>-dimensional grid, we give a novel definition of <i>digital rays dig(op)</i> from <i>o</i> to each grid point <i>p</i>. Each digital ray dig(<i>op</i>) approximates the Euclidean line segment <i>op</i> between <i>o</i> and <i>p</i>. The set of all digital rays satisfies a set of axioms analogous to the Euclidean(More)
1 In this paper we study a facility location problem in the plane in which a single point (facility) 2 and a rapid transit line (highway) are simultaneously located in order to minimize the total travel 3 time of the clients to the facility, using the L1 or Manhattan metric. The rapid transit line is 4 represented by a line segment with fixed length and(More)
We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP(More)
This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time. For general polygonal domains with h ≥ 1, however, no algorithm for computing the geodesic diameter was(More)
In memory-constrained algorithms, access to the input is restricted to be read-only, and the number of extra variables that the algorithm can use is bounded. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose main memory consumption takes the form of a stack into memory-constrained algorithms. Given(More)
A constant-work-space algorithm has read-only access to an input array and may use only O(1) additional words of O(log n) bits, where n is the input size. We show how to triangulate a plane straight-line graph with n vertices in O(n) time and constant workspace. We also consider the problem of preprocessing a simple n-gon P for shortest path queries, where(More)
We consider a topology control problem in which we are given a set of sensors in R and we would like to assign a communication radius to each of them so that they generate a connected network and have low receiver-based interference (defined as the largest in-degree of the network). We show that any radii assignment that generates a connected network can be(More)
We study a variation of the 1-center problem in which, in addition to a single supply facility, 8 we are allowed to locate a highway. This highway increases the transportation speed between any demand 9 point and the facility. We show that we can find the optimal location of both the facility and the highway 10 in O(n) or O(n log n) time, depending on(More)
Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-todescribe(More)