We give a randomized polynomial time algorithm with approximation ratio O(log φ(n)) for weighted set multi-cover instances with a shallow cell complexity of at most f(n, k) = nφ(n)k. Up to constant factors, this matches a recent result of Könemann et al. for the set cover case, i.e. when all the covering requirements are 1. One consequence of this is an O(1)-approximation for geometric weighted...

In many real-world transportation systems, passengers are often required to make a number of interchanges between different modes of transport. As cities continue to grow, a greater number of these connections tend to occur within centrally located Transport Hubs. In order to encourage the uptake of public transport in major cities, it is important for passengers to be able to connect between t...

The Soft-Capacitated Facility Location Problem, where each facility is composed of a variable number of fixed-capacity production units, has been recently studied in several papers, especially in the metric case. In this paper, we only consider the general problem where connection costs do not systematically satisfy the triangle inequality property. We show that an adaptation of the set coverin...

We consider the replica placement problem: given a graph with clients and nodes, place replicas on a minimum set of nodes to serve all the clients; each client is associated with a request and maximum distance that it can travel to get served and there is a maximum limit (capacity) on the amount of request a replica can serve. The problem falls under the general framework of capacitated set cov...

The Capacitated Arc Routing Problem (CARP) is a well-known and fundamental vehicle routing problem. A promising exact solution approach to the CARP is to model it as a set covering problem and solve it via branch-cut-and-price. The bottleneck in this approach is the pricing (column generation) routine. In this paper, we note that most CARP instances arising in practical applications are defined...

Clear cell renal cell carcinoma (ccRCC) is the most common solid lesion within kidneys, and its prognostic is influenced by the progression covering a complex network of gene interactions. In our study, a weighted gene co‑expression network was constructed to identify gene modules associated with the progression of ccRCC (n=35). In the significant module (R2 = -0.53), a total of 13 network hub ...

in this paper we present the problem of designing a three level hub center network. in our network, the top level consists of a complete network where a direct link is between all central hubs.  the second and third levels consist of star networks that connect the hubs to central hubs and the demand nodes to hubs and thus to central hubs, respectively. we model this problem in an incomplete net...

In a column-restricted covering integer program (CCIP), all the non-zero entries of any column of the constraint matrix are equal. Such programs capture capacitated versions of covering problems. In this paper, we study the approximability of CCIPs, in particular, their relation to the integrality gaps of the underlying 0,1-CIP. If the underlying 0,1-CIP has an integrality gap O(γ), and assumin...