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Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach [article]

Eric Angel IBISC, University d'Evry Val d'Essonne, France Stony Brook University, Stony Brook, NY, USA)
2016 arXiv   pre-print
While the k-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor.  ...  In this paper, we study the k-forest problem in the model of resource augmentation.  ...  The primal-dual approach is particularly well-suited to analyze algorithms with resource augmentation.  ... 
arXiv:1611.07489v1 fatcat:ghudfvx7pzf5xds2lr2wmgar5i

Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship [article]

Ioannis Caragiannis, Aris Filos-Ratsikas, Soren Kristoffer Stiil Frederiksen, Kristoffer Arnsfelt Hansen, Zihan Tan
2016 arXiv   pre-print
We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation.  ...  Our results suggest that even a limited augmentation of the resources can have wondrous effects on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation  ...  Our main conceptual contribution is the adoption of a resource augmentation approach to approximate mechanism design.  ... 
arXiv:1602.08023v1 fatcat:pruwdfoqdrahrk6adwsv4xib7a

Consensus-based Distributed Discrete Optimal Transport for Decentralized Resource Matching [article]

Rui Zhang, Quanyan Zhu
2019 arXiv   pre-print
We further derive primal and dual algorithms by exploring the primal and dual problems of discrete optimal transport with linear utility functions and prove the equivalence between them.  ...  In this paper, we take a consensus-based approach to decentralize discrete optimal transport problems and develop fully distributed algorithms with alternating direction method of multipliers.  ...  Distributed Dual Algorithm We have obtained a fully distributed primal algorithm to solve problem (23) with ADMM as shown in Proposition 3, and we can also obtain a fully distributed dual algorithm to  ... 
arXiv:1904.04318v1 fatcat:m3qnfxtmqjditnu7azgfjwscse

On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique

Reuven Bar-Yehuda, Dror Rawitz
2005 SIAM Journal on Discrete Mathematics  
Recently, primal-dual algorithms were divised by first constructing a local ratio algorithm, and then transforming it into a primal-dual algorithm.  ...  We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique.  ...  A primal-dual approximation algorithm typically constructs an approximate primal solution and a feasible dual solution simultaneously.  ... 
doi:10.1137/050625382 fatcat:bzp63mgnjna3bczhfzmqdarl6a

On the Equivalence between the Primal-Dual Schema and the Local-Ratio Technique [chapter]

Reuven Bar-Yehuda, Dror Rawitz
2001 Lecture Notes in Computer Science  
Recently, primal-dual algorithms were divised by first constructing a local ratio algorithm, and then transforming it into a primal-dual algorithm.  ...  We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique.  ...  A primal-dual approximation algorithm typically constructs an approximate primal solution and a feasible dual solution simultaneously.  ... 
doi:10.1007/3-540-44666-4_7 fatcat:prueocv4mjhznkmmkjvijxjzru

Decentralizing Coordination in Open Vehicle Fleets for Scalable and Dynamic Task Allocation

Marin Lujak, Stefano Giordani, Andrea Omicini, Sascha Ossowski
2020 Complexity  
We give a comparison and critical analysis of recent research results focusing on centralized, distributed, and decentralized solution approaches.  ...  problem, the semiassignment problem, the assignment problem with side constraints, and the assignment problem while recognizing agent qualification; all while considering the main aspect of open vehicle  ...  Primal-Dual Algorithms. Primal-dual algorithms start from a dual feasible solution (u, v) .  ... 
doi:10.1155/2020/1047369 fatcat:ctckxllr7fhxhlx2d67nqp2pkq

Approximation algorithm with constant ratio for stochastic prize-collecting Steiner tree problem

Jian Sun, Haiyun Sheng, Yuefang Sun, Donglei Du, Xiaoyan Zhang
2021 Journal of Industrial and Management Optimization  
Our main contribution is to present a primal-dual 3-approximation algorithm for this problem. 2020 Mathematics Subject Classification. Primary: 90C27, 68W25.  ...  Compared with deterministic optimization problem, it is an optimization problem with random factors, and requires the use of tools such as probability and statistics, stochastic process and stochastic  ...  In this paper, we consider the stochastic prize-collecting Steiner tree problem with polynomial scenarios and propose a 3-approximation algorithm based on the primal-dual technique.  ... 
doi:10.3934/jimo.2021116 fatcat:vlha4fkpfzfi7aqizyxup2pqse

Combining Progressive Hedging with a Frank--Wolfe Method to Compute Lagrangian Dual Bounds in Stochastic Mixed-Integer Programming

Natashia Boland, Jeffrey Christiansen, Brian Dandurand, Andrew Eberhard, Jeff Linderoth, James Luedtke, Fabricio Oliveira
2018 SIAM Journal on Optimization  
We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints.  ...  The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual value  ...  In order to make SDM efficient when used with PH to solve problem (9) , the minimization of the augmented Lagrangian dual problem can be solved approximately.  ... 
doi:10.1137/16m1076290 fatcat:mknhlkxdjnfsbf75gh4472wfva

Combining Progressive Hedging with a Frank-Wolfe Method to Compute Lagrangian Dual Bounds in Stochastic Mixed-Integer Programming [article]

Natashia Boland, Jeffrey Christiansen, Brian Dandurand, Andrew Eberhard, Jeff Linderoth, James Luedtke
2017 arXiv   pre-print
We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints.  ...  The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual value  ...  As iterative primal-dual approaches, methods based on the AL method or ADMM are more effective in practice.  ... 
arXiv:1702.00880v1 fatcat:b47qejvma5de3gzxi6vtpzh4z4

Local ratio

Reuven Bar-Yehuda, Keren Bendel, Ari Freund, Dror Rawitz
2004 ACM Computing Surveys  
The local ratio technique is closely related to the primal-dual schema, though it is not based on weak LP duality (which is the basis of the primal-dual approach) since it is not based on linear programming  ...  We trace the evolution path of the technique since its inception in the 1980's, culminating with the most recent development, namely, fractional local ratio, which can be viewed as a new LP rounding technique  ...  Connection to the Primal-Dual Schema The primal-dual schema for approximation algorithms is a widely used LPbased method for the design and analysis of approximation algorithms.  ... 
doi:10.1145/1041680.1041683 fatcat:hgkada6xvndpbl2bftj4gnzq4a

Algorithms for Optimization Problems in Planar Graphs (Dagstuhl Seminar 16221)

Jeff Erickson, Philip N. Klein, Dániel Marx, Claire Mathieu, Marc Herbstritt
2016 Dagstuhl Reports  
do this (resource augmentation).  ...  Subsequently, we reduce the initial problem to a question on primal-dual linkages that can be answered using suitable extensions of the irrelevant vertex technique for primal-dual graphs.  ...  Especially, it is possible to use a faster implementation of Dijkstra algorithm created by Fakcharoenphol and Rao in 2001.  ... 
doi:10.4230/dagrep.6.5.94 dblp:journals/dagstuhl-reports/EricksonKMM16 fatcat:wasdfgivt5fqdppfxo3iqqs2ta

Approximation Algorithms for NP-Hard Optimization Problems [chapter]

Philip Klein, Neal Young
2009 Algorithms and Theory of Computation Handbook, Second Edition, Volume 1  
A primal-dual approach, generalized from an algorithm for the Steiner forest problem, yields good performance guarantees for problems in this class.  ...  Primal-dual algorithms -witnesses via duality. For the purposes of approximation, solving a linear program exactly is often unnecessary.  ...  Further Information For an excellent survey of the field of approximation algorithms, focusing on recent results and research issues, see the survey by David Shmoys (Shmoys, ) .  ... 
doi:10.1201/9781584888239-c34 fatcat:kso5qt7qtvfrfp3ppym2lm532i

Machine Learning for Electricity Market Clearing [article]

Laurent Pagnier, Robert Ferrando, Yury Dvorkin, Michael Chertkov
2022 arXiv   pre-print
dispatches and locational marginal prices (LMPs), which are primal and dual solutions of the OPF optimization, respectively.  ...  resources (loads and renewables) to the binding lines, and supplement it with an efficient power-grid aware linear map to optimal dispatch and LMPs.  ...  ACKNOWLEDGMENT The authors would like to collectively acknowledge with gratitude the ARPA-E PERFORM grant from which this work arose. In addition, R.  ... 
arXiv:2205.11641v1 fatcat:6fijp4dzgvg7loqko3fkbb75ky

Support Vector Regression [chapter]

Mariette Awad, Rahul Khanna
2015 Efficient Learning Machines  
The central path is determined by solving the primal and dual optimization problems simultaneously.  ...  approach directly computes the posterior probability distributions p C x k | ( ) without computing the joint probability distribution p(x, C k ). a discriminant approach produces a mapping from the datapoints  ... 
doi:10.1007/978-1-4302-5990-9_4 fatcat:ufacii64ajcmtcfykwr6op6epm

Varying impacts of letters of recommendation on college admissions: Approximate balancing weights for subgroup effects in observational studies [article]

Eli Ben-Michael, Avi Feller, Jesse Rothstein
2021 arXiv   pre-print
We then show that this approach has a dual representation as a form of inverse propensity score weighting with a hierarchical propensity score model.  ...  We find that the impact of letters of recommendation increases with the predicted probability of admission, with mixed evidence of differences for under-represented minority applicants.  ...  We therefore augment with random forests, a nonlinear outcome estimator.  ... 
arXiv:2008.04394v2 fatcat:yz5zoptnrfdmvoriwf457vdknm
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