Packing and covering a tree by subtrees
Combinatorica
Integer and combinatorial optimization
Integer and combinatorial optimization
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
On the complexity of cooperative solution concepts
Mathematics of Operations Research
On some optimization problems on k-trees and partial k-trees
Discrete Applied Mathematics
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Randomized algorithms
On the nucleolus of the basic vehicle routing game
Mathematical Programming: Series A and B
On the complexity of testing membership in the core of min-cost spanning tree games
International Journal of Game Theory
Approximating the throughput of multiple machines under real-time scheduling
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Greedy strikes back: improved facility location algorithms
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Aspects of the Core of Combinatorial Optimization Games
Mathematics of Operations Research
Approximation algorithms
On dependent randomized rounding algorithms
Operations Research Letters
Complexity of constructing solutions in the core based on synergies among coalitions
Artificial Intelligence
Sharing the cost of multicast transmissions in wireless networks
Theoretical Computer Science
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Encouraging Cooperation in Sharing Supermodular Costs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Line Segment Facility Location in Weighted Subdivisions
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
A Cost-Sharing Method for the Soft-Capacitated Economic Lot-Sizing Game
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
A Stochastic Programming Duality Approach to Inventory Centralization Games
Operations Research
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Complexity of constructing solutions in the core based on synergies among coalitions
Artificial Intelligence
Non-cooperative facility location and covering games
Theoretical Computer Science
Buyer-supplier games: optimization over the core
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Competitive cost sharing with economies of scale
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Some new cooperative coverage facility location games
Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions
Operations Research
Network Design and Allocation Mechanisms for Carrier Alliances in Liner Shipping
Operations Research
Buyer-games: Optimization over the core
Theoretical Computer Science
Strategic cooperation in cost sharing games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
On the complexity of core, kernel, and bargaining set
Artificial Intelligence
Cooperative location games based on the minimum diameter spanning Steiner subgraph problem
Discrete Applied Mathematics
Noncooperative facility location games
Operations Research Letters
A cost-sharing method for an economic lot-sizing game
Operations Research Letters
Allocating Cost of Service to Customers in Inventory Routing
Operations Research
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The location of facilities in order to provide service for customers is a well-studied problem in the operations research literature. In the basic model, there is a predefined cost for opening a facility and also for connecting a customer to a facility, the goal being to minimize the total cost. Often, both in the case of public facilities (such as libraries, municipal swimming pools, fire stations,....) and private facilities (such as distribution centers, switching stations, ....), we may want to find a 'fair' allocation of the total cost to the customers-this is known as the cost allocation problem. A central question in cooperative game theory is whether the total cost can be allocated to the customers such that no coalition of customers has any incentive to build their own facility or to ask a competitor to service them. We establish strong connections between fair cost allocations and linear programming relaxations for several variants of the facility location problem. In particular, we show that a fair cost allocation exists if and only if there is no integrality gap for a corresponding linear programming relaxation; this was only known for the simplest unconstrained variant of the facility location problem. Moreover, we introduce a subtle variant of randomized rounding and derive new proofs for the existence of fair cost allocations for several classes of instances. We also show that it is in general NP-complete to decide whether a fair cost allocation exists and whether a given allocation is fair.