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Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class [article]

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, Andrew van der Poel
2018 arXiv   pre-print
The idea is to edit a given graph via vertex- or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution  ...  We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common  ...  Acknowledgments We thank Abida Haque and Adam Hesterberg for helpful initial discussions, Nicole Wein for providing helpful references on bounded degeneracy problems, and Michael O'Brien for helpful comments  ... 
arXiv:1806.02771v3 fatcat:p26xojkm2jd3xcrowcx4aoxeyq

Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, Andrew Van Der Poel, Michael Wagner
2019 European Symposium on Algorithms  
The idea is to edit a given graph via vertex-or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution  ...  We develop a framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common  ...  Acknowledgements We thank Abida Haque and Adam Hesterberg for helpful initial discussions, Nicole Wein for providing helpful references on bounded degeneracy problems, and Michael O'Brien for helpful comments  ... 
doi:10.4230/lipics.esa.2019.37 dblp:conf/esa/DemaineGKLLSVP19 fatcat:sa6gr2pm3rggpdb5pehdxtmk6e

Provable randomized rounding for minimum-similarity diversification

Bruno Ordozgoiti, Ananth Mahadevan, Antonis Matakos, Aristides Gionis
2022 Data mining and knowledge discovery  
We leverage this result to design an efficient randomized algorithm that provides a lower-order additive approximation guarantee.  ...  Even though this obstacle can be overcome using dependent rounding, we show that it is possible to obtain provably good solutions using an independent approach, which is faster, simpler to implement and  ...  give a 2-approximation to a maximization objective similar to ours (Borodin et al. 2017) , a result later extended to semimetrics (Zadeh and Ghadiri 2015) . He et al.  ... 
doi:10.1007/s10618-021-00811-2 pmid:35401029 pmcid:PMC8964643 fatcat:pxuab3fu7vhytnr536unxbnbwm

A Semidefinite Programming Approach to Side Chain Positioning with New Rounding Strategies

Bernard Chazelle, Carl Kingsford, Mona Singh
2004 INFORMS journal on computing  
We introduce two novel rounding schemes and provide theoretical justification for their effectiveness under various conditions.  ...  S ide chain positioning is an important subproblem of the general protein-structure-prediction problem, with applications in homology modeling and protein design.  ...  In addition, we have investigated how the rounding formulations behave on two classes of random graphs.  ... 
doi:10.1287/ijoc.1040.0096 fatcat:wynz7wbz4jcbxom6dkfulklcti

Convergence Rates of Smooth Message Passing with Rounding in Entropy-Regularized MAP Inference [article]

Jonathan N. Lee, Aldo Pacchiano, Michael I. Jordan
2020 arXiv   pre-print
This paper leverages recent work in entropy-regularized LPs to analyze convergence rates of a class of edge-based smooth message passing algorithms to ϵ-optimality in the relaxation.  ...  Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference.  ...  Acknowledgements We thank the anonymous reviewers and Marco Pavone for their invaluable feedback.  ... 
arXiv:1907.01127v2 fatcat:5jtlpe332vcszocewxsnhoi7p4

Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round [article]

Paul Dütting, Thomas Kesselheim, Éva Tardos
2015 arXiv   pre-print
Our goal is to show that a wide class of approximation algorithms yields this way mechanisms with low Price of Anarchy.  ...  In this paper we significantly extend the class of algorithms for which such a result is available by showing that this close connection between approximation ratio on the one hand and Price of Anarchy  ...  Clearly, a relax-and-round algorithm based on an αapproximate oblivious rounding scheme is an α-approximation algorithm. Mechanism Design Basics.  ... 
arXiv:1511.09208v1 fatcat:r7clduspyjeq7ito6tzrnsnuia

Toward accurate polynomial evaluation in rounded arithmetic [article]

James Demmel, Ioana Dumitriu, Olga Holtz
2006 arXiv   pre-print
Given a multivariate real (or complex) polynomial p and a domain D, we would like to decide whether an algorithm exists to evaluate p(x) accurately for all x ∈ D using rounded real (or complex) arithmetic  ...  This model is the traditional one used to analyze the accuracy of floating point algorithms.Our ultimate goal is to establish a decision procedure that, for any p and D, either exhibits an accurate algorithm  ...  Acknowledgments We are grateful to Bernd Sturmfels, Gautam Bharali, Plamen Koev, William (Velvel) Kahan, and Gregorio Malajovich for interesting discussions, to Jonathan Dorfman for his help with the graphs  ... 
arXiv:math/0508350v2 fatcat:lqnwvc4fn5bitb775mo6s55iyu

Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding

Shaddin Dughmi, Tim Roughgarden, Qiqi Yan
2016 Journal of the ACM  
Both of our mechanisms are instantiations of a new framework for designing approximation mechanisms based on randomized rounding algorithms.  ...  rounding algorithm.  ...  Finally, we thank the anonymous STOC and EC referees for helpful suggestions.  ... 
doi:10.1145/2908735 fatcat:5mk6xkjj2rh7zpnf2w43mann3y

Desynchronization: The Theory of Self-Organizing Algorithms for Round-Robin Scheduling

Ankit Patel, Julius Degesys, Radhika Nagpal
2007 First International Conference on Self-Adaptive and Self-Organizing Systems (SASO 2007)  
Here we present two biologically-inspired algorithms for achieving desynchronization: DESYNC and INVERSE-MS.  ...  To our knowledge, the theory of self-organizing desynchronization algorithms is presented here for the first time.  ...  Time and convergence rates for several DESYNC variants (n = 25 nodes, 200 rounds, near-synchronized initial condition randomly chosen within T /100 fraction of phase, α = 0.95). (a) Phase vs.  ... 
doi:10.1109/saso.2007.17 dblp:conf/saso/PatelDN07 fatcat:avcyc2rrgjb4ldttlwlcffzzxi

Structural Tractability of Counting of Solutions to Conjunctive Queries [article]

Arnaud Durand, Stefan Mengel
2013 arXiv   pre-print
classes of queries for which counting the number of solutions is tractable.  ...  We finally show how to compute an approximation of quantified star size in polynomial time where the approximation ratio depends on the width of the input.  ...  Acknowledgements The authors are grateful for the very helpful feedback on this paper they got from the reviewers of the conference version.  ... 
arXiv:1303.2059v1 fatcat:ahzo2x22hze45oywnj3yxeyk4y

Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning [article]

Scott Sussex
2021 arXiv   pre-print
By establishing novel submodularity properties of these objectives, we provide approximation guarantees for our algorithms.  ...  Causal structure learning is a key problem in many domains. Causal structures can be learnt by performing experiments on the system of interest.  ...  Thank you to Raj Agrawal for a helpful discussion regarding experiments. Experiments were performed on the Leonhard cluster managed by the HPC team at ETH Zürich  ... 
arXiv:2105.14024v2 fatcat:qktahxzzzresdersc6gwjtcdfy

Structural Tractability of Counting of Solutions to Conjunctive Queries

Arnaud Durand, Stefan Mengel
2014 Theory of Computing Systems  
classes of queries for which counting the number of solutions is tractable.  ...  We finally show how to compute an approximation of quantified star size in polynomial time where the approximation ratio depends on the width of the input.  ...  The authors are grateful for the very helpful feedback on this paper they got from the reviewers.  ... 
doi:10.1007/s00224-014-9543-y fatcat:vc27wzgxsrerdf7wezw5iecaci

Structural tractability of counting of solutions to conjunctive queries

Arnaud Durand, Stefan Mengel
2013 Proceedings of the 16th International Conference on Database Theory - ICDT '13  
classes of queries for which counting the number of solutions is tractable.  ...  We finally show how to compute an approximation of quantified star size in polynomial time where the approximation ratio depends on the width of the input.  ...  The authors are grateful for the very helpful feedback on this paper they got from the reviewers.  ... 
doi:10.1145/2448496.2448508 dblp:conf/icdt/DurandM13 fatcat:dhoxjmalhjfs3fotscsnyps2za

Fast determination of structurally cohesive subgroups in large networks

Robert S. Sinkovits, James Moody, B. Tolga Oztan, Douglas R. White
2016 Journal of Computational Science  
We describe here an approach that exploits the properties of cliques, k-cores and vertex separators to iteratively reduce the complexity of the graph to the point where standard algorithms can be used  ...  Structurally cohesive subgroups are a powerful and mathematically rigorous way to characterize network robustness.  ...  JM was partially supported by NIH grant NICHD HD075712 Models and Tools for Dynamic Health-Relevant Diffusion over Complex Networks.  ... 
doi:10.1016/j.jocs.2016.10.005 pmid:28503215 pmcid:PMC5423759 fatcat:sbxpqugsp5cphlk5airzyyl4eu

Polynomial-time algorithms for Multimarginal Optimal Transport problems with structure [article]

Jason M. Altschuler, Enric Boix-Adsera
2022 arXiv   pre-print
For structures (2)-(3), we give the first poly(n,k) time algorithms, even for approximate computation. Together, these three structures encompass many -- if not most -- current applications of MOT.  ...  We illustrate this ease-of-use by developing poly(n,k) time algorithms for three general classes of MOT cost structures: (1) graphical structure; (2) set-optimization structure; and (3) low-rank plus sparse  ...  Acknowledgements We are grateful to Jonathan Niles-Weed, Pablo Parrilo, and Philippe Rigollet for insightful conversations; to Frederic Koehler for suggesting a simpler proof of Lemma 3.7; to Ben Edelman  ... 
arXiv:2008.03006v4 fatcat:pmd3ghf5ozdw3k52mafykpf4ei
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