Improved Bounds for Metric Capacitated Covering Problems

Primal-Dual Schema for Capacitated Covering Problems

Primal-dual algorithms have played an integral role in recent developments in approximation algorithms, and yet there has been little work on these algorithms in the context of LP relaxations that have been strengthened by the addition of more sophisticated valid inequalities. We introduce primal-dual schema based on the LP relaxations devised by Carr, Fleischer, Leung & Phillips for the minimu...

Lower Bounds for Covering Problems

Convergent Dual Bounds Using an Aggregation of Set-Covering Constraints for Capacitated Problems

Extended formulations are now widely used to solve hard combinatorial optimization problems. Such formulations have prohibitively-many variables and are generally solved via Column Generation (CG). CG algorithms are known to have frequent convergence issues, and, up to a sometimes large number of iterations, classical Lagrangian dual bounds may be weak. This paper is devoted to set-covering pro...

Improved Bounds for Covering Complete Uniform Hypergraphs

We consider the problem of covering the complete r-uniform hypergraphs on n vertices using complete r-partite graphs. We obtain lower bounds on the size of such a covering. For small values of r our result implies a lower bound of Ω( e r r √ r n log n) on the size of any such covering. This improves the previous bound of Ω(rn log n) due to Snir [5]. We also obtain good lower bounds on the size ...

A Min-Edge Cost Flow Framework for Capacitated Covering Problems

In this work, we introduce the Cov-MECF framework, a special case of minimum-edge cost flow in which the input graph is bipartite. We observe that several important covering (and multi-covering) problems are captured in this unifying model and introduce a new heuristic LPO for any problem in this framework. The essence of LPO harnesses as an oracle the fractional solution in deciding how to gre...