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Faster Provable Sieving Algorithms for the Shortest Vector Problem and the Closest Vector Problem on Lattices in ℓp Norm

Priyanka Mukhopadhyay
2021 Algorithms  
In this work, we give provable sieving algorithms for the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP) on lattices in ℓp norm (1≤p≤∞).  ...  The running time we obtain is better than existing provable sieving algorithms. We give a new linear sieving procedure that works for all ℓp norm (1≤p≤∞).  ...  The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  ... 
doi:10.3390/a14120362 fatcat:2brqjjy76jabjkg4th4rfsebse

The SCIP Optimization Suite 8.0 [article]

Ksenia Bestuzheva, Mathieu Besançon, Wei-Kun Chen, Antonia Chmiela, Tim Donkiewicz, Jasper van Doornmalen, Leon Eifler, Oliver Gaul, Gerald Gamrath, Ambros Gleixner, Leona Gottwald, Christoph Graczyk (+23 others)
2021 arXiv   pre-print
Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints  ...  presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack.  ...  In particular, thanks go to Suresh Bolusani, Didier Chételat, Gregor Hendel, Andreas Schmitt, Helena Völker, Robert Schwarz, Matthias Miltenberger, Matthias Walter, and Antoine Prouvoust and the Ecole  ... 
arXiv:2112.08872v1 fatcat:fqkdhu4bhngcblzaaaasqneplm

Cost-to-Go Function Approximation [chapter]

2017 Encyclopedia of Machine Learning and Data Mining  
Mitchell's, (1982; candidate-elimination algorithm performs a bidirectional search in the hypothesis space.  ...  These two sets form two boundaries on the version space.  ...  In this case, the resulting theory is interpreted as a decision list. In the following, we will assume a two-class problem with a positive and a negative class.  ... 
doi:10.1007/978-1-4899-7687-1_100093 fatcat:vse7ncdqs5atlosjhz7fhlj3im

Some Fundamental Theorems in Mathematics [article]

Oliver Knill
2022 arXiv   pre-print
An expository hitchhikers guide to some theorems in mathematics.  ...  Differential equations A differential equation d dt x = f (x) and x(0) = x 0 in a Banach space (X, || • ||) (a normed, complete vector space) defines an initial value problem: we look for a solution x(  ...  Examples are the the integer factoring problem. An efficient algorithm for the first one would have enormous consequences.  ... 
arXiv:1807.08416v4 fatcat:lw7lbsxyznfrnaozilxapihmdy

st Symposium on Simplicity in Algorithms New Orleans LA, USA Co-located with The 29th ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)

Raimund Seidel
2018 unpublished
Ravi and Madhur Tulsiani for helpful discussions and comments on the presentation. Acknowledgement.  ...  In an earlier version of the proof of Theorem 3, we erroneously claimed that, conditioned on the current sampling rate being 1/2 j , edges in E t α had been sampled at that rate.  ...  The two most important computational problems on lattices are the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP).  ... 

Graph-Based Approaches to Protein StructureComparison - From Local to Global Similarity

Marco Mernberger, Mathematik Und Informatik, Hüllermeier, Eyke (Prof.)
In this thesis, several conceptually different algorithmic approaches have been developed, based on local, global and semi-global strategies, for the task of comparing protein structure data, more specifically  ...  Drawing upon structural information allows the inference of function for unknown proteins even in cases where no apparent homology can be found on the sequence level.  ...  Let the length of the shortest path be defined by lp(v i , v j ) with: lp(v i , v j ) = k−1 l=1 w(v φ l , v φ l +1 ) . ( 4.15) Testing for equality on real-valued edge weights would obviously not be  ... 
doi:10.17192/z2012.0057 fatcat:dp6ivnp2anc5tgvwovekx5q4fq

1th Conference on the Theory of Quantum Computation, Communication and Cryptography LIPIcs-Leibniz International Proceedings in Informatics

Anne Broadbent, Anne Broadbent, Pascal Weil, Reinhard Wilhelm
2016 unpublished
We thank Dave Touchette for helpful comments on the manuscript. A.A. thanks Rahul Jain and Guo Yalei for helpful discussions. A.G. thanks Mohammed Acknowledgements.  ...  The author is supported by the EU projects SIQS and QALGO, and thanks Anne Broadbent, Harry Buhrman, Yfke Dulek and Christian Schaffner for useful discussions.  ...  Furthermore, Regev [13] showed that the unique shortest vector problem reduces to the dihedral coset problem, so it could provide a pathway for finding a quantum algorithm for lattice problems.  ...