Mathematical Programming: Series A and B
Structure of a simple scheduling polyhedron
Mathematical Programming: Series A and B
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximate Core Allocation for Binpacking Games
SIAM Journal on Discrete Mathematics
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
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
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
Limitations of cross-monotonic cost sharing schemes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
SIAM Journal on Discrete Mathematics
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We study the computational complexity and algorithmic aspects of computing the least core value of supermodular cost cooperative games, and uncover some structural properties of the least core of these games. We provide motivation for studying these games by showing that a particular class of optimization problems has supermodular optimal costs. This class includes a variety of problems in combinatorial optimization, especially in machine scheduling. We show that computing the least core value of supermodular cost cooperative games is NP-hard, and design approximation algorithms based on oracles that approximately determine maximally violated constraints. We apply our results to schedule planning games, or cooperative games where the costs arise from the minimum sum of weighted completion times on a single machine. By improving upon some of the results for general supermodular cost cooperative games, we are able to give an explicit formula for an element of the least core of schedule planning games, and design a fully polynomial time approximation scheme for computing the least core value of these games.