Minimum cost arborescences

Dutta, Bhaskar; Mishra, Debasis

doi:10.1016/j.geb.2011.05.007

Cited by 23 publications

(10 citation statements)

References 16 publications

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“…• Minimum-cost spanning tree problems where some agents are indifferent (Trudeau 2014c), i.e., they can connect to the source (and get rewarded for it) if it helps others agents. • Arborescences (Dutta and Mishra 2012;Bahel and Trudeau 2017), where the costs are not symmetric, i.e., c i j = c ji in general. • Minimum-cost spanning tree problems where the costs are uncertain and represented by closed intervals (Moretti et al 2011).…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

Cid

Puga

2021

SERIEs

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Minimum-cost spanning tree problems are well-known problems in the operations research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused, mainly, in studying how to allocate the connection cost among the agents. We review the papers that have addressed the allocation problem using cooperative game theory. We also relate the rules defined through cooperative games with rules defined directly from the problem, either through algorithms for computing a minimal tree, either through a cone-wise decomposition.

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Section: Conclusion and Future Researchmentioning

confidence: 99%

A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

Cid

Puga

2021

SERIEs

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“…The stand-alone core stability and efficiency are two traditional properties in the network literature [4,10,16,17]; while routing-proofness is a relatively more recent idea [5,10,18]. The predecessor of routing-proofness was first coined the axiom of no transit originated by Hanriet and Moulin in [5].…”

Section: Related Literaturementioning

confidence: 99%

Routing-Proofness in Congestion-Prone Networks

Juárez

2019

Games

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We consider the problem of sharing the cost of connecting a large number of atomless agents in a network. The centralized agency elicits the target nodes that agents want to connect, and charges agents based on their demands. We look for a cost-sharing mechanism that satisfies three desirable properties: efficiency which charges agents based on the minimum total cost of connecting them in a network, stand-alone core stability which requires charging agents not more than the cost of connecting by themselves directly, and limit routing-proofness which prevents agents from profitable reporting as several agents connecting from A to C to B instead of A to B. We show that these three properties are not always compatible for any set of cost functions and demands. However, when these properties are compatible, a new egalitarian mechanism is shown to satisfy them. When the properties are not compatible, we find a rule that meets stand-alone core stability, limit routing-proofness and minimizes the budget deficit.

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“…• we can use directed edges in mcst and require a directed path from the source to each agent (Dutta and Mishra, 2011); ditto in traveling salesman and facility location; • we can require more demanding connectivity constraints in mcst or mc-Steiner-t:…”

Section: Combinatorial Optimization Gamesmentioning

confidence: 99%

Cost Sharing in Networks: Some Open Questions

Moulin

2013

Int. Game Theory Rev.

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The fertile application of cooperative game techniques to cost sharing problems on networks has so far concentrated on the Stand Alone core test of fairness and/or stability, and ignored many combinatorial optimization problems where this core can be empty. I submit there is much room for an axiomatic discussion of fair division in the latter problems, where Stand Alone objections are not implementable. But the computational complexity of optimal solutions is still a very severe obstacle to this approach.

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Minimum cost arborescences

Cited by 23 publications

References 16 publications

A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

Routing-Proofness in Congestion-Prone Networks

Cost Sharing in Networks: Some Open Questions

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