We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on the vertex set, which are cost, capacity, and demand. The objective of this problem is to compute a demand assignment of least cost, such that the demand of e...

We study the partial capacitated vertex cover problem (pcvc) in which the input consists of a graphG and a covering requirement L. Each edge e in G is associated with a demand (or load) l(e), and each vertex v is associated with a (soft) capacity c(v) and a weight w(v). A feasible solution is an assignment of edges to vertices such that the total demand of assigned edges is at least L. The weig...

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on the vertex set, which are cost, capacity, and demand. The objective of this problem is to compute a demand assignment of least cost, such that the demand of e...

In this paper, we consider generalizations of classical covering problems to handle hard capacities. In the hard capacitated set cover problem, additionally each set has a covering capacity which we are not allowed to exceed. In other words, after picking a set, we may cover at most a specified number of elements. Based on the classical results by Wolsey, an O(log n) approximation follows for t...

We studied the following two geometric optimization problems with cardinality constraints. • Capacitated covering with unit balls: Given a set of n points in R and a positive integer L, partition them into a minimum number of groups such that each group contains at most L points, and can be covered by a unit ball in R. • Capacitated connected dominating set in unit disk graph: Given a positive ...

The Lasserre/Sum-of-Squares hierarchy is a systematic procedure to strengthen LP relaxations by constructing a sequence of increasingly tight formulations. For a wide variety of optimization problems, this approach captures the convex relaxations used in the best available approximation algorithms. The capacitated covering IP is an integer program of the form min{cx : Ux ≥ d, 0 ≤ x ≤ b, x ∈ Z+}...

One main group of a transportation network is a discrete hub covering problem that seeks to minimize the total transportation cost. This paper presents a multi-product and multi-mode hub covering model, in which the transportation time depends on travelling mode between each pair of hubs. Indeed, the nature of products is considered different and hub capacity constraint is also applied. Due to ...