The assignment game introduced by Shapley and Shubik (1972)  is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the goods. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to fewer agents.
The feasibility pump (FP) has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems. Briefly, FP alternates between two sequences of points: one of feasible solutions for the relaxed problem, and another of integer points. This short paper extends FP, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem.
In a recent work [J. Castro, J. Cuesta, Quadratic regularizations in an interior-point method for primal block-angular problems, Mathematical Programming, in press (doi:10.1007/s10107-010-0341-2)] the authors improved one of the most efficient interior-point approaches for some classes of block-angular problems. This was achieved by adding a quadratic regularization to the logarithmic barrier. This regularized barrier was shown to be self-concordant, thus fitting the general structural optimization interior-point framework. In practice, however, most codes implement primal dual path-following algorithms. This short paper shows that the primal-dual regularized central path is well defined, i.e., it exists, it is unique, and it converges to a strictly complementary primal dual solution.
For different reliability importance measures we prove that the criticality relation between nodes can completely determine the most important component in a system. In particular, we prove that in k-out-of-n systems, the ranking of component reliabilities determines the ranking of component importance for, at least, three different reliability importance measures.