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Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach
[article]
2016
arXiv
pre-print
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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]
2016
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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
2005
SIAM Journal on Discrete Mathematics
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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]
2001
Lecture Notes in Computer Science
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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
2020
Complexity
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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
2021
Journal of Industrial and Management Optimization
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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
2018
SIAM Journal on Optimization
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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]
2017
arXiv
pre-print
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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
2004
ACM Computing Surveys
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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)
2016
Dagstuhl Reports
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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]
2009
Algorithms and Theory of Computation Handbook, Second Edition, Volume 1
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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]
2022
arXiv
pre-print
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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]
2015
Efficient Learning Machines
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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]
2021
arXiv
pre-print
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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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