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Sums and products along sparse graphs [article]

Noga Alon, Omer Angel, Itai Benjamini, Eyal Lubetzky
2009 arXiv   pre-print
We proceed to give lower and upper bounds for this problem in different settings. In addition, we provide tight bounds for sums along expanders.  ...  n^1/2+δ for its sum-product over the integers implies a lower bound of n^1+δ for the original Erdős-Szemerédi problem.  ...  This work was initiated while the second and third authors were visiting the Theory Group of Microsoft Research.  ... 
arXiv:0905.0135v4 fatcat:ueztglxy3bebzjxrw2bfkq73ju

Sums and products along sparse graphs

Noga Alon, Omer Angel, Itai Benjamini, Eyal Lubetzky
2011 Israel Journal of Mathematics  
We proceed to give lower and upper bounds for this problem in different settings. In addition, we provide tight bounds for sums along expanders.  ...  n 1/2+δ for its sum-product over the integers implies a lower bound of n 1+δ for the original Erdős-Szemerédi problem.  ...  We also thank an anonymous referee for valuable comments. This work was initiated while the second and third authors were visiting the Theory Group of Microsoft Research.  ... 
doi:10.1007/s11856-011-0170-x fatcat:vw6nz4o4tzebtdfjnk2fn6qgbu

Low-rank matrix completion and denoising under Poisson noise [article]

Andrew D. McRae, Mark A. Davenport
2020 arXiv   pre-print
We show that for all three estimators, with high probability, we have an upper error bound (in the Frobenius norm error metric) that depends on the matrix rank, the fraction of the elements observed, and  ...  We furthermore show that the above results are minimax optimal (within a universal constant) in classes of matrices with low rank and bounded row and column sums.  ...  When do the upper and lower bounds match? Within multiplicative constants, the lower bounds of Theorems 3 and 4 match the approximate upper bound of (5).  ... 
arXiv:1907.05325v2 fatcat:3vm7xaw2sfachh2u6h4m4eczua

Page 2070 of Mathematical Reviews Vol. , Issue 81F [page]

1981 Mathematical Reviews  
Using familiar linear algebra techniques, the author proves that the. di- mension of this subspace is n?— 2n—1. From this an upper bound on the number of magic squares with entries from {1,2,---, n?}  ...  is derived, namely, the upper bound (n”)! /(8-(2n + 1)!). The his- tory of magic squares is briefly sketched in the introduction. The interested reader should also consult J. Dénes and A. D.  ... 

Query complexity in expectation [article]

Jedrzej Kaniewski, Troy Lee, Ronald de Wolf (CWI, University of Amsterdam)
2014 arXiv   pre-print
As an example we give an exponentially-close entrywise approximation of the slack matrix of the perfect matching polytope with psd-rank only 2^n^1/2+epsilon.  ...  Since query complexity can be used to upper bound communication complexity of related functions, we can derive some upper bounds on psd extension complexity by constructing efficient quantum query algorithms  ...  us a version of [LRS14] .  ... 
arXiv:1411.7280v1 fatcat:qqpeu43kjnejfg5ipo24zxdkze

On the additivity of preference aggregation methods [article]

László Csató
2015 arXiv   pre-print
It turns out that least squares and generalized row sum with an appropriate parameter choice preserve the relative ranking of two objects if the ranking problems added have the same comparison structure  ...  Therefore some directions of weakening consistency are suggested, and several ranking methods, the score, generalized row sum and least squares as well as fair bets and its two variants (one of them entirely  ...  Here m = 3 and n = 3, therefore the reasonable upper bound of ε is 1/3.  ... 
arXiv:1512.00421v1 fatcat:abqspwmldzemxkvf3xybbnuo7y

Query Complexity in Expectation [chapter]

Jedrzej Kaniewski, Troy Lee, Ronald de Wolf
2015 Lecture Notes in Computer Science  
As an example we give an exponentially-close entrywise approximation of the slack matrix of the perfect matching polytope with psd-rank only 2 n 1/2+ε .  ...  Since query complexity can be used to upper bound communication complexity of related functions, we can derive some upper bounds on psd extension complexity by constructing efficient quantum query algorithms  ...  us a version of [LRS14] .  ... 
doi:10.1007/978-3-662-47672-7_62 fatcat:a6fesbjv45fi3ehtxfmewvcj24

Page 2473 of Mathematical Reviews Vol. , Issue 89E [page]

1989 Mathematical Reviews  
*/2], The lower bound is obtained by generalizing Tuerberg’s rank of quadratic form argument for the k =2 problem. The upper bound follows from a recursive construction.  ...  Upper bounds for the number of perfect matchings in hexagonal systems are deduced. They depend on the number of vertices and edges of the hexagonal system.  ... 

On the ranking of a Swiss system chess team tournament

László Csató
2017 Annals of Operations Research  
The tournament is represented as a ranking problem such that the linearly-solvable row sum (score), generalized row sum, and least squares methods have favourable axiomatic properties.  ...  The paper argues for the use of least squares method with a results matrix favouring match points on the basis of its relative insensitivity to the choice between match and board points, retrodictive accuracy  ...  Acknowledgements We are grateful to two anonymous referees for their valuable comments and suggestions.  ... 
doi:10.1007/s10479-017-2440-4 fatcat:h7z2p4g4ffe7tojfeggbujnnju

Improved Analysis of RANKING for Online Vertex-Weighted Bipartite Matching [article]

Billy Jin, David P. Williamson
2020 arXiv   pre-print
We consider the generalization of the RANKING algorithm for this problem introduced by Huang, Tang, Wu, and Zhang (TALG 2019), who show that their algorithm has a competitive ratio of 0.6534.  ...  In this paper, we consider the online vertex-weighted bipartite matching problem in the random arrival model.  ...  It would also be interesting to derive an improved upper bound for this problem.  ... 
arXiv:2007.12823v1 fatcat:gg53szwi4zfapl2g6sdctjpafu

The square root rank of the correlation polytope is exponential [article]

Troy Lee, Zhaohui Wei
2014 arXiv   pre-print
The square root rank is an upper bound on the positive semidefinite rank of a matrix, and corresponds the special case where all matrices in the factorization are rank-one.  ...  The square root rank of a nonnegative matrix A is the minimum rank of a matrix B such that A=B ∘ B, where ∘ denotes entrywise product.  ...  The motivation for studying square root rank is that it is an upper bound on the positive semidefinite rank [GPT13, Zha12] .  ... 
arXiv:1411.6712v1 fatcat:rbgwpyqbfbfbjj2kyk6jtrl5ri

Distributed Estimation of Generalized Matrix Rank: Efficient Algorithms and Lower Bounds [article]

Yuchen Zhang, Martin J. Wainwright, Michael I. Jordan
2015 arXiv   pre-print
The upper bound is matched by an Ω(n) lower bound on the randomized communication complexity. We demonstrate the practical effectiveness of the proposed algorithm with some numerical experiments.  ...  We study the following generalized matrix rank estimation problem: given an n × n matrix and a constant c ≥ 0, estimate the number of eigenvalues that are greater than c.  ...  Acknowledgements MJW and YZ were partially supported by the ONR-MURI grant DOD 002888 from the Office of Naval Research. MIJ and YZ were partially supported by the U. S.  ... 
arXiv:1502.01403v2 fatcat:dp7r5vwmgbgbviuezzgh54wgbu

Fitting discrete multivariate distributions with unbounded marginals and normal-copula dependence

Athanassios N. Avramidis
2009 Proceedings of the 2009 Winter Simulation Conference (WSC)  
Furthermore, we propose a simple method for truncating the support while controlling the error via the bound, which is a sum of scaled squared tail probabilities.  ...  Our main contribution is an upper bound on the absolute error, where error is defined as the difference between r and the resulting rank correlation between the original unbounded marginals.  ...  ACKNOWLEDGMENTS I thank professor Pierre L'Ecuyer for his valuable comments on an earlier draft of the paper.  ... 
doi:10.1109/wsc.2009.5429352 dblp:conf/wsc/Avramidis09 fatcat:bq3qkg3kafhaviy2chcnwg3ws4

Rank minimization over finite fields

Vincent Y. F. Tan, Laura Balzano, Stark C. Draper
2011 2011 IEEE International Symposium on Information Theory Proceedings  
The reliability function associated to the minimum-rank decoder is also derived. Our bounds hold even in the case where the sensing matrices are sparse. Connections to rank-metric codes are discussed.  ...  This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it.  ...  upper bound in (2) .  ... 
doi:10.1109/isit.2011.6033722 dblp:conf/isit/TanBD11 fatcat:gcstzavxgrd5ja4iwhuv44sufm

Book announcements

1992 Discrete Applied Mathematics  
A special case: the unbounded knapsack problem (Upper bounds and approximate algoritlr,ns. Exact algorithms. An exact algorithm for large-size problems. Computational experiments).  ...  Chuprer 4: Subser-Sum Problem. Introduction. Exact algorithms (Dynamic programming. A hybrid algorithm. An afgorithm for large-size problems). Approximate algorithms (Greedy algorithms.  ... 
doi:10.1016/0166-218x(92)90042-9 fatcat:tmyols4labfmpb2xgcevnbkl6y
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