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Parallel algorithms and concentration bounds for the Lovasz Local Lemma via witness DAGs [article]

Bernhard Haeupler, David G. Harris
2015 arXiv   pre-print
The Lovász Local Lemma (LLL) is a cornerstone principle in the probabilistic method of combinatorics, and a seminal algorithm of Moser & Tardos (2010) provides an efficient randomized algorithm to implement  ...  We also provide improved and tighter bounds on the run-times of the sequential and parallel resampling-based algorithms originally developed by Moser & Tardos.  ...  of the Lovász Local Lemma.  ... 
arXiv:1509.06430v2 fatcat:qjldmsdsuvdvdficgrie37d7ne

Derandomizing the Lovasz Local Lemma via log-space statistical tests [article]

David G. Harris
2019 arXiv   pre-print
The Lovász Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection B of "bad" events which are mostly independent and have  ...  We describe an alternate deterministic parallel (NC) algorithm for the LLL, based on a general derandomization method of Sivakumar (2002) using log-space statistical tests.  ...  Acknowledgements Thanks to Aravind Srinivasan for helpful discussions, and for pointing me to the method of Sivakumar.  ... 
arXiv:1807.06672v2 fatcat:geqtokw7avde5hh2hsqnxbulbu

New bounds for the Moser-Tardos distribution [article]

David G. Harris
2019 arXiv   pre-print
The Lovasz Local Lemma (LLL) is a probabilistic tool which has been used to show the existence of a variety of combinatorial structures with good "local" properties.  ...  One can similarly define an "MT-distribution" for these algorithms, that is, the distribution of the configuration they produce.  ...  LLL is by far the most common setting in combinatorics, there are other probability spaces for which a generalized form of the LLL, known as the Lopsided Lovász Local Lemma or LLLL, applies.  ... 
arXiv:1610.09653v7 fatcat:cux3gjmm5vhfdemsjaqnc6fb7i

Toward a Model for Backtracking and Dynamic Programming

Michael Alekhnovich, Allan Borodin, Joshua Buresh-Oppenheim, Russell Impagliazzo, Avner Magen, Toniann Pitassi
2011 Computational Complexity  
After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and  ...  We propose a model called priority branching trees (pBT ) for backtracking and dynamic programming algorithms.  ...  Special thanks to Alberto Marchetti-Spaccamela for contributing the upper bound of Theorem 10, and to Charles Rackoff for going above and beyond the call of helpful comments.  ... 
doi:10.1007/s00037-011-0028-y fatcat:p33blz7c2vgo3hy52imzwkzvkq

Cryptography in a Quantum World [article]

Stephanie Wehner
2008 arXiv   pre-print
Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a quantum computer is  ...  How does the presence of entanglement affect classical protocols? And, what limitations does entanglement impose on implementing quantum protocols?  ...  We concentrate on the case of mutually unbiased bases, as this case is most relevant to our initial goal of analyzing protocols for quantum cryptography in the bounded storage model [DFSS05] .  ... 
arXiv:0806.3483v1 fatcat:br4tirmaundxnbvud3cjdoamgy

Toward a Model for Backtracking and Dynamic Programming

M. Alekhnovich, A. Borodin, J. Buresh-Oppenheim, R. Impagliazzo, A. Magen, T. Pitassi
20th Annual IEEE Conference on Computational Complexity (CCC'05)  
After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and  ...  We propose a model called priority branching trees (pBT ) for backtracking and dynamic programming algorithms.  ...  Special thanks to Alberto Marchetti-Spaccamela for contributing the upper bound of Theorem 10, and to Charles Rackoff for going above and beyond the call of helpful comments.  ... 
doi:10.1109/ccc.2005.32 dblp:conf/coco/AlekhnovichBBIMP05 fatcat:dbiez4lqbvgltmjvf3eaxzw52u

Matching minors in bipartite graphs [article]

Sebastian Wiederrecht, Technische Universität Berlin, Stephan Kreutzer
2022
In this thesis we adapt fundamental parts of the Graph Minors series of Robertson and Seymour for the study of matching minors and investigate a connection to the study of directed graphs.  ...  in polynomial time on graphs of bounded width.  ...  a bounded width decomposition as a witness, plays a major part in the question whether perfect matching width can be used for algorithmic applications at all.  ... 
doi:10.14279/depositonce-14958 fatcat:ag65eqvyxjdspf4se6ams3ab7m

LIPIcs, Volume 32, SNAPL'15, Complete Volume [article]

Thomas Ball, Rastislav Bodik, Shriram Krishnamurthi, Benjamin S. Lerner, Greg Morrisett
2015
Excellence in Algorithms; and by funding from Intel and AT&T.  ...  We thank Josef Widder for the fruitful discussions on this subject, Heather Miller and Philipp Haller for their help with the pickling library, and the anonymous reviewers for their comments.  ...  One promising candidate is the Lovász Local Lemma [12] , which gives a better bound when each event is independent of most of the other events.  ... 
doi:10.4230/lipics.snapl.2015 fatcat:ljoxwa7wp5achn2tbrmpriez7y

2014 Jahresbericht Annual Report

Registernummer Amtsgericht, Saarbrücken Hrb, Vorsitzender Des Aufsichtsrates, Ing, Jähnichen Stefan, Raimund Geschäftsführung, Seidel, Heike Meißner, Technisch-Administrative Geschäftsführerin, Gesellschafter
unpublished
The seminar was organized into seven sessions: frameworks and languages; algorithm configuration; constraints in pattern mining; learning constraints; machine learning with constraints; applications; and  ...  The demonstrations presented at the seminar were by: Guido Tack  ...  James Currie realized that shuffle squares can indeed be avoided applying the Lovász Local Lemma in his argument.  ... 
fatcat:jojclrrbifa2lgyh3ux4tv7tiu

Dagstuhl Reports, Volume 8, Issue 1, January 2018, Complete Issue [article]

2018
I wish to thank Eli Biham for discussions related to conditional linear cryptanalysis and Céline Blondeau for suggestions how to improve the presentation.  ...  -Symmetric Cryptography Acknowledgments The authors acknowledge the Dagstuhl Committee for providing the excellent facility and environment that are inducive for fruitful discussions.  ...  Lifting Monotone Circuit Lower Bounds from Resolution This result is essentially a lifting theorem for "decision dags" and "dag communication protocols."  ... 
doi:10.4230/dagrep.8.1 fatcat:dv5ntjliznbs7dwohrcmiwr3lm

Dagstuhl Reports, Volume 7, Issue 4, April 2017, Complete Issue [article]

2018
This allows us to construct two semi-algorithms, one searching for a proof of equivalence, one for a witness of non-equivalence.  ...  Frank Drewes then discussed the notion of graph transformations, and especially of DAGs, and proposed in his talk a definition of DAG transducers.  ...  , simple linear-time algorithm.  ... 
doi:10.4230/dagrep.7.4 fatcat:oiz7wwh4hbhtvkg773gx65qukm