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A Primal-Dual Approximation Algorithm for Partial Vertex Cover: Making Educated Guesses

Julián Mestre
2007 Algorithmica  
The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. We provide a primal-dual 2-approximation algorithm which runs in O(n log n+m) time.  ...  We study the partial vertex cover problem.  ...  Acknowledgment: Thanks to Samir Khuller for suggesting developing an algorithm for partial vertex cover that does not use exhaustive guessing and for many useful comments on earlier versions of the paper  ... 
doi:10.1007/s00453-007-9003-z fatcat:ffpevhpx7vfpdbxwcwli2qgr7i

A Primal-Dual Approximation Algorithm for Partial Vertex Cover: Making Educated Guesses [chapter]

Julián Mestre
2005 Lecture Notes in Computer Science  
The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. We provide a primal-dual 2-approximation algorithm which runs in O(n log n+m) time.  ...  We study the partial vertex cover problem.  ...  Acknowledgment: Thanks to Samir Khuller for suggesting developing an algorithm for partial vertex cover that does not use exhaustive guessing and for many useful comments on earlier versions of the paper  ... 
doi:10.1007/11538462_16 fatcat:46nxowr24raships3tcpz24bjy

Approximation of Partial Capacitated Vertex Cover

Reuven Bar-Yehuda, Guy Flysher, Julián Mestre, Dror Rawitz
2010 SIAM Journal on Discrete Mathematics  
We study the partial capacitated vertex cover problem (pcvc) in which the input consists of a graph G and a covering requirement L.  ...  Our algorithms are based on a unified approach for designing and analyzing approximation algorithms for capacitated covering problems.  ...  Acknowledgments We thank Einat Or for helpful discussions. We also thank Roee Engelberg for his suggestions.  ... 
doi:10.1137/080728044 fatcat:7l2vaom4y5fwdl6g64cjvhhabm

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  A stabilization technique based on partial pivoting is proposed and it is shown that it can be used for stabilization of primal, dual and primal-dual interior point methods.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

Linear Programming: Foundations and Extensions

R J Vanderbei
1998 Journal of the Operational Research Society  
The simple yet beautiful idea of modifying the Kojima-Mizuno-Yoshise primal-dual algorithm to make it into a one-phase algorithm is due to Lustig (1990) .  ...  Associated with each connected planar network is a dual network defined by interchanging vertices and faces. That is, place a dual vertex in the center of each primal face.  ...  The important point is that these legs are defined by market demand, and it is therefore not clear a priori how to put these legs together in such a way that the available aircraft can cover all of them  ... 
doi:10.1038/sj.jors.2600987 fatcat:d4xmw4dy7rflnextmoz2bytkqa

Mass Conservative Domain Decomposition for Porous Media Flow [chapter]

Jan M., Eirik Keilegavlen, Andreas Sandvi
2012 Finite Volume Method - Powerful Means of Engineering Design  
the fine grid, and contains exactly one vertex (cell on level 0) of the dual coarse grid, see Fig. 2 .  ...  We make a few comments about the Schur complement system.  ... 
doi:10.5772/38700 fatcat:sq4x7m6invhjverdywpo6cfgoy

Community detection and stochastic block models: recent developments [article]

Emmanuel Abbe
2017 arXiv   pre-print
The note also covers some of the algorithms developed in the quest of achieving the limits, in particular two-round algorithms via graph-splitting, semi-definite programming, linearized belief propagation  ...  tradeoff for partial recovery, the learning of the SBM parameters and the gap between information-theoretic and computational thresholds.  ...  Acknowledgements I would to thank my collaborators from the main papers discussed in the manuscript, in particular, A. Bandeira, G. Hall, C. Sandon, Y. Deshpande, A.  ... 
arXiv:1703.10146v1 fatcat:fxbi227nqna4xiugshm5jbpdna

Approximation of Partial Capacitated Vertex Cover [chapter]

Reuven Bar-Yehuda, Guy Flysher, Julián Mestre, Dror Rawitz
Algorithms – ESA 2007  
We study the partial capacitated vertex cover problem (pcvc) in which the input consists of a graph G and a covering requirement L.  ...  Our algorithms are based on a unified approach for designing and analyzing approximation algorithms for capacitated covering problems.  ...  Acknowledgments We thank Einat Or for helpful discussions. We also thank Roee Engelberg for his suggestions.  ... 
doi:10.1007/978-3-540-75520-3_31 dblp:conf/esa/Bar-YehudaFMR07 fatcat:5oidsocuvjembadlpptkvgj6qm

Applications of semi-definite optimization in quantum information protocols [article]

Piotr Mironowicz
2018 arXiv   pre-print
The results include a new type of quantum key distribution protocol based on Hardy's paradox; several protocols for quantum random number expansion; a method of formulation of SDP relaxations of SDI protocols  ...  ; and a DI Santha-Vazirani source of randomness amplification protocol.  ...  Formulation of the primal-dual interior point algorithm In this section we give an overview of working of a predictor-corrector path-following interior point algorithm for SDP.  ... 
arXiv:1810.05145v1 fatcat:rmzt7v32ubhttgbcw7zhiuzupa

Minimum color‐degree perfect b ‐matchings

Mariia Anapolska, Christina Büsing, Martin Comis, Tabea Krabs
2020 Networks  
The last speaker of the session will chair the session, with two exceptions for PhD-only sessions: Combinatorial Optimization (Mon 18, Room PP, 16-17) chaired by R.  ...  Conversely, if a speaker ends before the time is up, you should encourage some questions/discussion/debate: e.g. invite questions from the audience and leave a pause long enough to be slightly awkward,  ...  On the way to obtaining the kernelization algorithm, we also provide a 2-approximation algorithm for γ-matching.  ... 
doi:10.1002/net.21974 fatcat:4qgtutmxrrcy7anvxks4fivcii

Physics inspired algorithms for (co)homology computations of three-dimensional combinatorial manifolds with boundary

Paweł Dłotko, Ruben Specogna
2013 Computer Physics Communications  
Drawing inspiration from low-frequency electrodynamics, this paper presents a physics inspired algorithm for first cohomology group computations on three-dimensional complexes.  ...  In [20], a dual version of the Kotiuga's algorithm -called Generalized Spanning Tree Technique (GSTT) -has been presented to compute the 1st cohomology group basis H 1 (M) ∼ = H 2 (M, ∂M) starting from  ...  The second author was partially supported by the Italian Ministry of Education, University and Research (MIUR) project PRIN 2009LTRYRE.  ... 
doi:10.1016/j.cpc.2013.05.006 fatcat:ua7lzesd4fh5bodrktfscxlgkq

Identity Matrix [chapter]

2013 Encyclopedia of Operations Research and Management Science  
An analysis technique used to analyze a queueing system that is not a continuous-time Markov chain.  ...  It appraises the system at selected time points which allow the system to be analyzed via a discrete-parameter Markov chain.  ...  Operational research for informed innovation: NHS direct as a case study in the design, implementation and evaluation of a New Public Service.  ... 
doi:10.1007/978-1-4419-1153-7_200302 fatcat:ph4et3usavg4zcpkzfp4yz5qlu

Lack of Memory [chapter]

2013 Encyclopedia of Operations Research and Management Science  
For example, the primal-dual predictorcorrector algorithm developed by Mehrotra (1992) established a structure that has commonly been adopted by subsequent algorithms.  ...  There are many useful relationships between the primal and dual problems, so the dual provides considerable information for analyzing the primal.  ...  The most widely known of these models is referred to as the maximal covering location problem (MCLP) or the partial covering problem, depending on the specific formulation.  ... 
doi:10.1007/978-1-4419-1153-7_200373 fatcat:yem4y7syhze2pjtf3sop5fhak4

Expander graphs and their applications

Shlomo Hoory, Nathan Linial, Avi Wigderson
2006 Bulletin of the American Mathematical Society  
These are extremely important for applications. There are algorithmic problems -given a graph, test if it is an expander with given parameters.  ...  From the probabilistic viewpoint, one considers the natural random walk on a graph, in which we have a token on a vertex, that moves at every step to a random neighboring vertex, chosen uniformly and independently  ...  Avi Wigderson is a professor at the Institute for Advanced Study in Princeton. Before that he was a professor of computer science at the Hebrew University for fifteen years.  ... 
doi:10.1090/s0273-0979-06-01126-8 fatcat:5u65bvautndzhnkhxurqrudqfy

The NP-Hardness of Covering Points with Lines, Paths and Tours and their Tractability with FPT-Algorithms

Apichat Heednacram, University, My, Vladimir Estivill-Castro, Francis Suraweera
2018
However, with the Line Cover problem we demonstrate that it is not dicult to adapt algorithms for the decision version to algorithms for the optimization version.  ...  We also implement several algorithms for the Line Cover problem and conduct experimental evaluations of our algorithms with respect to previously known algorithms.  ...  Acknowledgements I would like to thank the Australian Government, Department of Education, Employment and Workplace Relations (DEEWR) for awarding me the Endeavour Postgraduate Award.  ... 
doi:10.25904/1912/1694 fatcat:zif4xnvchrbpdnsm6on63aez64
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