Related papers: Covering compact metric spaces greedily
We empirically analyze a simple heuristic for large sparse set cover problems. It uses the weighted greedy algorithm as a basic building block. By multiplicative updates of the weights attached to the elements, the greedy solution is…
Simple random coverage models, well studied in Euclidean space, can also be defined on a general compact metric space. By analogy with the geometric models, and with the discrete coupon collector's problem and with cover times for finite…
More precise estimation of the greedy algorithm complexity for a special case of the set cover problem is given in this paper.
Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the…
Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension,…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
Structural parameters of graph (such as degeneracy and arboricity) had rarely been considered when designing algorithms for $\textit{(edge) clique cover}$ problems. Taking degeneracy of graph into account, we present a greedy framework and…
In this article, we consider the following capacitated covering problem. We are given a set $P$ of $n$ points and a set $\mathcal{B}$ of balls from some metric space, and a positive integer $U$ that represents the capacity of each of the…
This paper proposes a greedy algorithm named as Big step greedy set cover algorithm to compute approximate minimum set cover. The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains…
We present a method to obtain upper bounds on covering numbers. As applications of this method, we reprove and generalize results of Rogers on economically covering Euclidean $n$-space with translates of a convex body, or more generally,…
Considering the set cover problem, by modifying the approach that gives a logarithmic approximation guarantee for the greedy algorithm, we obtain an estimation of the greedy algorithm's accuracy for a particular input. We compare the…
We address the problem of efficient and unobstructed surveillance or communication in complex environments. On one hand, one wishes to use a minimal number of sensors to cover the environment. On the other hand, it is often important to…
Compact packings are specific packings of spheres which can be seen as tilings and are good candidates to maximize the density. We show that the compact packings of the Euclidean space with two sizes of spheres are exactly those obtained by…
Methodology is provided towards the solution of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the d-dimensional Euclidean…
In this paper, we present our heuristic solutions to the problems of finding the maximum and minimum area polygons with a given set of vertices. Our solutions are based mostly on two simple algorithmic paradigms: greedy method and local…
We discuss construction of coverings of the unit ball of a finite dimensional Banach space. The well known technique of comparing volumes gives upper and lower bounds on covering numbers. This technique does not provide a construction of…
Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
We describe the structure of the different hexagonal grids in dimension d=3, propose short notation for them, investigate the contact numbers of ball packings in these grids and share some computational results up to 200 balls, using mainly…