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We study the Maximum Flow Network Interdiction Problem (MFNIP). We present two classes of polynomially separable valid inequalities for Cardinality MFNIP. We also prove the integrality gap of the LP relaxation of Wood's [19] integer program is not bounded by a constant factor, even when the LP relaxation is strengthened by our valid inequalities. Finally,… (More)

We study stochastic linear programming games: a class of stochastic cooperative games whose payoffs under any realization of uncertainty are determined by a specially structured linear program. These games can model a variety of settings, including inventory centralization and cooperative network fortification. We focus on the core of these games under an… (More)

Extended Abstract Consider a situation where a group of agents wishes to share the costs of their joint actions, and needs to determine how to distribute the costs amongst themselves in a fair manner. For example, a set of agents may agree to process their jobs together on a machine, and share the optimal cost of scheduling these jobs. This kind of… (More)

We study minimizing the sum of weighted completion times in a concurrent open shop. We give a primal–dual 2-approximation algorithm for this problem. We also show that several natural linear programming relaxations for this problem have an integrality gap of 2. Finally, we show that this problem is inapproximable within a factor strictly less than 6/5 if P… (More)

- Moses Charikar, Klaus Jansen, Omer Reingold, Jose D.R Rolim, Ashkan Aazami, Michael D. Stilp +33 others
- 2008

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract We study the approximation of the least core value and the least core of supermodular cost cooperative games. We provide a framework for approximation based on oracles that approximately determine maximally violated constraints.… (More)

5 We consider the economic lot-sizing game with general concave ordering cost functions. It is 6 well-known that the core of this game is nonempty when the inventory holding costs are linear. 7 The main contribution of this work is a combinatorial, primal-dual algorithm that computes a cost 8 allocation in the core of these games in polynomial time. We also… (More)

We study cooperative games with supermodular costs. We show that supermodular costs arise in a variety of situations; in particular, we show that the problem of minimizing a linear function over a supermodular polyhedron—a problem that often arises in combinatorial optimization—has supermodular optimal costs. In addition, we examine the computational… (More)

We study scheduling as a means to address the increasing energy concerns in manufacturing enterprises. In particular, we consider a flow shop scheduling problem with a restriction on peak power consumption, in addition to the traditional time-based objectives. We investigate both mathematical programming and combinatorial approaches to this scheduling… (More)

We consider cooperative traveling salesman games with non-negative asymmetric costs satisfying the triangle inequality. We construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric traveling salesman problem, using the parsimonious property and a previously unknown connection to linear… (More)