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- Approximation guarantees of Median Mechanism in $\\mathbb{R}^d$
The coordinate-wise median is a classic and most well-studied strategy-proof mechanism in social choice and facility location scenarios Surprisingly, there is no systematic study of its approximation ratio in d -dimensional spaces
- Optimality of the coordinate-wise median mechanism for . . . - Springer
In Sect 3, we discuss the optimality of the coordinate-wise median mechanism In Sects 4 and 5, we discuss the problem of finding the approximation ratio of the coordinate-wise median mechanism for the utilitarian objective and the p -norm objective Section 6 concludes
- publications | Jianhao Jia
The coordinate-wise median is a classic and most well-studied strategy-proof mechanism in social choice and facility location scenarios Surprisingly, there is no systematic study of its approximation ratio in d-dimensional spaces
- (PDF) Optimality of the coordinate-wise median mechanism for . . .
We conjecture that the approximation ratio of coordinate-wise 1 median is actually equal to the lower bound 21− p (as is the case when p = 2 or p = ∞) If the conjecture is true, it would imply that coordinate-wise median is the best deterministic strategyproof mechanism for p-norm objective
- k-Median Clustering via Metric Embedding: Towards Better Initialization . . .
Abstract 1In clustering, the choice of initial centers is crucial for the convergence speed of the algorithms We propose a new initialization scheme for the k-median problem in the general metric space (e g , discrete space induced by graphs), based on the construction of metric embedding tree structure of the data We propose a novel and eficient search algorithm which finds initial centers
- Approximation algorithms for fair k-median problem without fairness . . .
The fair k -median problem is one of the important clustering problems The current best approximation ratio is 4 675 for this problem with 1-fairness violation, which was proposed by Bercea et al [APPROX-RANDOM'2019] To our best knowledge, there is no available approximation algorithm for this problem without any fairness violation in doubling metrics In this paper, we consider the fair k
- Random Cuts are Optimal for Explainable k-Medians - OpenReview
The paper studies the optimal upper bound of explainable k-median and shows a tight analysis for the random coordinate cut algorithm The explainable k-clustering model was first introduced by Dasgupta et al [ICML’20] and was followed by a flurry of work to understand the optimal approximation factor to achieve explainability
- Approximation Guarantees of Median Mechanism in Rd
The coordinate-wise median is a classic and most well-studied strategy-proof mechanism in social choice and facility location scenarios Surprisingly, there is no systematic study of its approx-imation ratio in -dimensional spaces
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