Lagrangian heuristic for simultaneous subsidization and penalization: implementations on rooted travelling salesman games

Zhou, Yuqian; Li, Zikang

doi:10.1007/s00186-022-00771-3

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…It has received quite some attention in the literature, e.g. [1,2,3,4,8,21,24,31,29,30,34,35]. Indeed, for games with empty core, maximizing x(N ) over the almost core is equivalent to computing the cost of stability, and also to computing some other minimal core relaxations proposed earlier in the literature; see Section 3 for details.…”

Section: Core and Almost Core For Tu Gamesmentioning

confidence: 99%

“…A related line of research [29] is to consider the strong ε-core relaxation parameterized by ε as given by the function ω(ε) := min x∈R n {c(N ) − x(N ) : x(S) ≤ c(S) + ε ∀S N } , and to approximate it computationally. This so-called "penalty-subsidy function" [29] is further studied in another variant in a follow up paper [30], there approximating it using Langragian relaxation techniques, and with computational results specifically for traveling salesperson games.…”

Section: Also Approximations Of ε ⋆mentioning

confidence: 99%

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Algorithmic Solutions for Maximizing Shareable Costs

Zhou¹,

Lin²,

Uetz³

et al. 2023

Preprint

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This paper addresses the optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game. This means that all subsets of agents have an outside option at a certain cost, and stability requires that the cost shares are defined so that none of the outside options is preferable. When maximizing total shareable costs, the cost shares must satisfy all constraints that define the core of a TU game, except for being budget balanced. The paper gives a fairly complete picture of the computational complexity of this optimization problem, in relation to classical computational problems on the core. We also show that, for games with an empty core, the problem is equivalent to computing minimal core relaxations for several relaxations that have been proposed earlier. As an example for a class of cost sharing games with non-empty core, we address minimum cost spanning tree games. While it is known that cost shares in the core can be found efficiently, we show that the computation of maximal cost shares is NP-hard for minimum cost spanning tree games. We also derive a 2-approximation algorithm. Our work opens several directions for future work.

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Section: Core and Almost Core For Tu Gamesmentioning

confidence: 99%

Section: Also Approximations Of ε ⋆mentioning

confidence: 99%

Algorithmic Solutions for Maximizing Shareable Costs

Zhou¹,

Lin²,

Uetz³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Algorithmic solutions for maximizing shareable costs

Zou,

Lin,

Uetz

et al. 2024

Networks

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This article addresses the linear optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game. When maximizing total shareable costs, the cost shares must satisfy all constraints that define the core of a TU game, except for being budget balanced. The article first gives a fairly complete picture of the computational complexity of this optimization problem, its relation to optimization over the core itself, and its equivalence to other, minimal core relaxations that have been proposed earlier. We then address minimum cost spanning tree (MST) games as an example for a class of cost sharing games with non‐empty core. While submodular cost functions yield efficient algorithms to maximize shareable costs, MST games have cost functions that are subadditive, but generally not submodular. Nevertheless, it is well known that cost shares in the core of MST games can be found efficiently. In contrast, we show that the maximization of shareable costs is ‐hard for MST games and derive a 2‐approximation algorithm. Our work opens several directions for future research.

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Lagrangian heuristic for simultaneous subsidization and penalization: implementations on rooted travelling salesman games

Cited by 2 publications

References 18 publications

Algorithmic Solutions for Maximizing Shareable Costs

Algorithmic Solutions for Maximizing Shareable Costs

Algorithmic solutions for maximizing shareable costs

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