A Lagrangian-based heuristic for the well-known Set Covering Problem (SCP), which won the first prize in the FASTER competition, and proposes a dynamic pricing scheme for the variables, akin to that used for solving large-scale LPs, to be coupled with subgradient optimization and greedy algorithms.Expand

We prove that the problem of sorting a permutation by the minimum number of reversals is NP-hard, thus answering a major question on the complexity of a problem which has widely been studied in the… Expand

A graph theoretic formulation for the train timetabling problem using a directed multigraph in which nodes correspond to departures/arrivals at a certain station at a given time instant is proposed, used to derive an integer linear programming model that is relaxed in a Lagrangian way.Expand

A transformation from MAX-ACD to MIN-SBR is described, which is therefore shown to be NP-hard as well, answering an outstanding question which has been open for some years.Expand

A powerful graph-theoretic relaxation of RMP is provided, essentially calling for a perfect matching in a graph that forms the maximum number of cycles jointly withq given perfect matchings.Expand

The main idea in the analysis is to use the fact that the fractional and integer BP solutions have almost the same value, which is implicit in the approximation schemes for the problem, as a stand-alone structural result that implies the existence of modified heights for the shelves whose sum yields approximately the number of bins needed to pack them.Expand

An exact branch-and-bound algorithm is proposed for QKP, where upper bounds are computed by considering a Lagrangian relaxation that is solvable through a number of (continuous) knapsack problems, and the algorithm is capable of solving reasonable-size Max Clique instances from the literature.Expand

This survey focuses on the most recent and effective algorithms for SCP, considering both heuristic and exact approaches, outlining their main characteristics and presenting an experimental comparison on the test-bed instances of Beasley's OR Library.Expand

In this paper we introduce a new general framework for set covering problems, based on the combination of randomized rounding of the (near-)optimal solution of the linear programming (LP) relaxation,… Expand