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Ranking and Unranking algorithms for Derangements Based On Lexicographical Order

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SSRN

SSRN 2024年

作者： Xie, Zhibo Wu, Ro-Yu Shi, Lingjuan School of Software Northwestern Polytechnical University Shaanxi Xi’an710072 China Department of Industrial Management Lunghwa University of Science and Technology Taoyuan333326 Taiwan

In this paper, we address the derangement problem by constructing a derangement table. We have identified the relationship between lexicographically ordered derangements and their coding trees through the derangement table, and also discovered the connection between the number of derangements and the number of permutations. Based on this derangement table, we have provided relevant formulas and proofs. The paper designs ranking and unranking algorithms for the lexicographical derangement problem using these formulas, with a time complexity of $O(nlogn)$ and a space complexity of $O(n^2)$. According to our investigation, among the existing research, there were no ranking and unranking algorithms for the lexicographical derangement problem with a time complexity of less than or equal to $O(nlogn)$. © 2024, The Authors. All rights reserved.

关键词： consensus algorithm

Reducing Diversity to Generate Hierarchical Archetypes

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arXiv 2024年

作者： Ibias, Alfredo Antona, Hector Ramirez-Miranda, Guillem Guinovart, Enric Alarcon, Eduard Avatar Cognition Barcelona Spain Universitat Politècnica de Catalunya - BarcelonaTech Barcelona Spain

The Artificial Intelligence field seldom address the development of a fundamental building piece: a framework, methodology or algorithm to automatically build hierarchies of abstractions. This is a key requirement in order to build intelligent behaviour, as recent neuroscience studies clearly expose. In this paper we present a primitive-based framework to automatically generate hierarchies of constructive archetypes, as a theory of how to generate hierarchies of abstractions. We assume the existence of a primitive with very specific characteristics, and we develop our framework over it. We prove the effectiveness of our framework through mathematical definitions and proofs. Finally, we give a few insights about potential uses of our framework and the expected results. © 2024, CC BY.

关键词： consensus algorithm

Global Fuzzy Adaptive consensus Control of Unknown Nonlinear Multiagent Systems

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2020年第3期28卷 510-522页

作者： Chen, Jiaxi Li, Junmin Yuan, Xinxin Xidian Univ Sch Math & Stat Xian 710071 Peoples R China

This paper investigates the global consensus problems for the first-order and second-order unknown nonlinear multiagent systems (MASs) with uncertain input disturbance. Fuzzy logic systems are applied to solve the global consensus problem for unknown nonlinear MASs. A fully distributed adaptive fuzzy control is designed to enable followers asymptotically to track the leader without using any dynamics of the leader. The global consensus conditions are also derived for the first-order and second-order unknown MASs, which overcomes the drawback of the semiglobal consensus in existing literature. It is worth mentioning that the proposed approach can greatly alleviate the computation burden because it only needs to update a few parameters. An efficient framework is also given to achieve the global formation control of the second-order unknown nonlinear MAS with an undirected connected graph. Finally, four simulated examples are given to illustrate the effectiveness of the proposed control protocols.

关键词： Protocols Symmetric matrices Artificial neural networks Adaptive control Fuzzy control Uncertainty Adaptive fuzzy control consensus algorithm formation control fuzzy logic systems (FLSs) multiagent systems (MAS)

MULTIDIMENSIONAL MOMENT PROBLEM AND DIAGONAL SCHUR algorithm

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arXiv 2025年

作者： Kovalyov, Ivan Universität Osnabrück Albrechtstr. 28a Osnabrück49076 Germany

The multidimensional moment problem is studied in terms of the Steiltjes transform. The diagonal step-by-step algorithm is constructed for the multidimensional moment problem. The set of solutions of the full multidimensional moment problem is found in terms of the continued fractions. Moreover, the diagonal step-by-step algorithm can be applied to the special truncated multidimensional moment problem. © 2025, CC BY.

关键词： consensus algorithm

Proxy Discrimination After Students for Fair Admissions

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arXiv 2025年

作者： Fagan, Frank South Texas College of Law Houston United States EDHEC Augmented Law Institute France

Law protects people from discrimination. algorithms, however, can easily circumvent the appearance of discrimination through the artful use of proxy variables. For instance, a lending algorithm may appear to satisfy a legal standard by ignoring race, but the same algorithm might deny loan applicants on the basis of having attended a particular high school—a variable that may closely correlate with race. An algorithm that assesses work performance and recommends promotions may ignore sex, but the same algorithm might penalize employees who take, on average, more paternity leave—a variable that may closely correlate with sex. The abuse of proxies cuts across political views on affirmative action. For example, an admissions committee might technically ignore race consistent with recent changes to Equal Protection rules, but the same committee might consider variables that are highly correlated to race, such as zip code, high school, and the income of parents, in order to achieve a university’s diversity goals. Today, there is no clear legal test for regulating the use of variables that proxy for race and other protected classes and classifications. This Article develops such a test. Decision tools that use proxies are narrowly tailored when they exhibit the weakest total proxy power. The test is necessarily comparative. Thus, if two algorithms predict loan repayment or university academic performance with identical accuracy rates, but one uses zip code and the other does not, then the second algorithm can be said to have deployed a more equitable means for achieving the same result as the first algorithm. Scenarios in which two algorithms produce comparable and non-identical results present a greater challenge. This Article suggests that lawmakers can develop caps to permissible proxy power over time, as courts and algorithm builders learn more about the power of variables. Finally, the Article considers who should bear the burden of producing less discriminatory alter

关键词： consensus algorithm

Transductive Conformal Inference for Ranking

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arXiv 2025年

作者： Fermanian, Jean-Baptiste Humbert, Pierre Blanchard, Gilles Université de Montpellier Inria France Sorbonne Université and Université Paris Cité CNRS Laboratoire de Probabilités Statistique et Modélisation France Université Paris Saclay Institut Mathématique d’Orsay France

We introduce a method based on Conformal Prediction (CP) to quantify the uncertainty of full ranking algorithms. We focus on a specific scenario where n + m items are to be ranked by some "black box" algorithm. It is assumed that the relative (ground truth) ranking of n of them is known. The objective is then to quantify the error made by the algorithm on the ranks of the m new items among the total (n + m). In such a setting, the true ranks of the n original items in the total (n + m) depend on the (unknown) true ranks of the m new ones. Consequently, we have no direct access to a calibration set to apply a classical CP method. To address this challenge, we propose to construct distribution-free bounds of the unknown conformity scores using recent results on the distribution of conformal p-values. Using these scores upper bounds, we provide valid prediction sets for the rank of any item. We also control the false coverage proportion, a crucial quantity when dealing with multiple prediction sets. Finally, we empirically show on both synthetic and real data the efficiency of our CP method. Copyright © 2025, The Authors. All rights reserved.

关键词： consensus algorithm

On reconstructing high derivatives of noisy time-series with confidence intervals

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arXiv 2025年

作者： Alamir, Mazen Univ. Grenoble Alpes CNRS Grenoble INP GIPSA-lab Grenoble38000 France

Reconstructing high derivatives of noisy measurements is an important step in many control, identification and diagnosis problems. In this paper, a heuristic is proposed to address this challenging issue. The framework is based on a dictionary of identified models indexed by the bandwidth, the noise level and the required degrees of derivation. Each model in the dictionary is identified via cross-validation using tailored learning data. It is also shown that the proposed approach provides heuristically defined confidence intervals on the resulting estimation. The performance of the framework is compared to the state-of-the-art available algorithms showing noticeably higher accuracy. Although the results are shown for up to the 4-th derivative, higher derivation orders can be used with comparable results. © 2025, CC BY.

关键词： consensus algorithm

New algorithms for the Pareto-Optimal Connected P-Centdian Problem and the Connected P-Centdian Problem on Block Graphs

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SSRN

SSRN 2025年

作者： Wang, Biing-Feng Li, Chih-Yu Chuang, Tzu-Yang Department of Computer Science National Tsing Hua University Hsinchu30013 Taiwan

This paper studies the problem of finding a set of p connected vertices in a block graph. The center and median criteria are considered at the same time. Two variants of the problem are discussed. One is called the Pareto-optimal connected p-centdian problem (P-CpCD), which is to find all Pareto-optimal solutions with respect to the center and the median functions;and the other is called the connected p-centdian problem (CpCD), which is to find a set of p connected vertices to minimize the convex combination of the center and the median functions with coefficients λ and 1 - λ, respectively, where λ ∈ [0, 1] is a given parameter. For CpCD on an unweighted block graph, Nguyen et al. [TCS 2022] had an O(n)-time algorithm for λ ∈ [1/2, 1] and left solving the problem in O(n) time for λ ∈ (0, 1/2) as an open problem. We answer this open problem affirmatively by providing an O(n)-time algorithm for any λ ∈ [0, 1]. For P-CpCD on an unweighted block graph, Kang et al. [J Comb Optim 2018] had an O(n^2)-time algorithm. We give an improved O(n + pN_out)-time algorithm, where N_out © 2025, The Authors. All rights reserved.

关键词： consensus algorithm

A Division algorithm for the Gaussian Integers’ Minimal Euclidean Function

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arXiv 2025年

作者： Graves, Hester IDA Center for Computing Sciences United States

The usual division algorithms on and [i] measure the size of remainders using the norm function. These rings are Euclidean with respect to several functions. The pointwise minimum of all Euclidean functions f: R \ 0 → on a Euclidean domain R is itself a Euclidean function, called the minimal Euclidean function and denoted by R. The integers, Z, and the Gaussians, [i], are the only rings of integers of number fields for which we have a formula to compute their minimal Euclidean functions, and [i]. This paper presents the first division algorithm for [i] relative to [i], empowering readers to perform the Euclidean algorithm on [i] using its minimal Euclidean *** Codes 11A05, 11A63, 11R04, 11R11, 11R99 Copyright © 2025, The Authors. All rights reserved.

关键词： consensus algorithm