Approximation algorithms for partially covering with edges

Approximation algorithms for partially covering with edges

The edge dominating set (EDS) and edge cover (EC) problems are classical graph covering problems in which one seeks a minimum cost collection of edges which covers the edges or vertices, respectively, of a graph. We consider the generalized partial cover version of these problems, in which failing to cover an edge, in the EDS case, or vertex, in the EC case, induces a penalty. The objective is ...

Approximation algorithms for covering/packing integer programs

Given matrices A and B and vectors a, b, c and d, all with non-negative entries, we consider the problem of computing min{cx : x ∈ Z+, Ax ≥ a, Bx ≤ b, x ≤ d}. We give a bicriteria-approximation algorithm that, given ε ∈ (0, 1], finds a solution of cost O(ln(m)/ε) times optimal, meeting the covering constraints (Ax ≥ a) and multiplicity constraints (x ≤ d), and satisfying Bx ≤ (1 + ε)b + β, wher...

Approximation Algorithms for Partial Covering Problems

We study a generalization of covering problems called partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example, in k-partial set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-partial set cover, if each element occurs in at most f sets, then we derive a primal...

Approximation algorithms for the covering Steiner problem

Approximation Algorithms for Covering Polygons with Squares and Similar Problems

We consider the problem of covering polygons, without any acute interior angles, using a preferably minimum number of squares. The squares must lie entirely within the polygon. Let P be an arbitrary input polygon, with n vertices, coverable by squares. Let (P) denote the minimum number of squares required to cover P. In the rst part of this paper we show an O(n log n+(P)) time algorithm which p...