Integer and combinatorial optimization
Integer and combinatorial optimization
Mathematical Programming: Series A and B
Structure of a simple scheduling polyhedron
Mathematical Programming: Series A and B
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
Some optimal inapproximability results
Journal of the ACM (JACM)
On the computation of the nucleolus of a cooperative game
International Journal of Game Theory
Single Machine Scheduling with Release Dates
SIAM Journal on Discrete Mathematics
Scheduling Unit Jobs with Compatible Release Dates on Parallel Machines with Nonstationary Speeds
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
Matching games: the least core and the nucleolus
Mathematics of Operations Research
Cooperative facility location games
Journal of Algorithms - Special issue: SODA 2000
Cost sharing in a job scheduling problem using the Shapley value
Proceedings of the 6th ACM conference on Electronic commerce
Preface to the Special Issue on Computational Economics
Operations Research
Polymatroid Optimization, Submodularity, and Joint Replenishment Games
Operations Research
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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 complexity of the least core and least core value of supermodular cost cooperative games. We show that the problem of computing the least core value of these games is strongly NP-hard and, in fact, is inapproximable within a factor strictly less than 17/16 unless P = NP. For a particular class of supermodular cost cooperative games that arises from a scheduling problem, we show that the Shapley value---which, in this case, is computable in polynomial time---is in the least core, while computing the least core value is NP-hard.