Monotone Covering Problems with an Additional Covering Constraint

Monotone Covering Problems with an Additional Covering Constraint

We provide preliminary results regarding the existence of a polynomial time approximation scheme (PTAS) for minimizing a linear function over a 0/1 covering polytope which is integral, with one additional covering constraint. Our algorithm is based on extending the methods of Goemans and Ravi for the constrained minimum spanning tree problem and, in particular, implies the existence of a PTAS f...

Covering symmetric semi-monotone functions

We define a new set of functions called semi-monotone, a subclass of skew-supermodular functions. We show that the problem of augmenting a given graph to cover a symmetric semi-monotone function is NP-complete if all the values of the function are in {0, 1} and we provide a minimax theorem if all the values of the function are different from 1. Our problem is equivalent to the node to area augm...

Covering Problems

Covering Problems with Hard Capacities

We consider the classical vertex cover and set cover problems with the addition of hard capacity constraints. This means that a set (vertex) can only cover a limited number of its elements (adjacent edges) and the number of available copies of each set (vertex) is bounded. This is a natural generalization of the classical problems that also captures resource limitations in practical scenarios. ...

Minimal Logical Constraint Covering Sets

We propose a general framework for computing minimal set covers under class of certain logical constraints. The underlying idea is to transform the problem into a mathematical programm under linear constraints. In this sense it can be seen as a natural extension of the vector quantization algorithm proposed by [5]. We show which class of logical constraints can be cast and relaxed into linear c...