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On Iterated Dominance, Matrix Elimination, and Matched Paths [article]

Felix Brandt, Felix Fischer, Markus Holzer
2010 arXiv   pre-print
We however establish connections to a matching problem along paths in a directed graph, which is computationally hard in general but can also be used to identify tractable cases of matrix elimination.  ...  The two-action case can be reformulated as a natural elimination problem on a matrix, the complexity of which turns out to be surprisingly difficult to characterize and ultimately remains open.  ...  We thank Hermann Gruber, Paul Harrenstein, Tim Roughgarden, Inbal Talgam, and Michael Tautschnig for valuable discussions, and apologize to Edith Hemaspaandra for spoiling the sunset at White Sands.  ... 
arXiv:1001.0529v1 fatcat:xw4z2geyqjca3kv4hqzsw4evd4

A new pivoting strategy for Gaussian elimination

Markus Olschowka, Arnold Neumaier
1996 Linear Algebra and its Applications  
This paper discusses a method for determining a good pivoting sequence for Gaussian elimination, based on an algorithm for ding assignment problems.  ...  which is a strongly diagonal dominant matrix and thus perfectly scaled for Gaussian elimination.  ...  The basic idea of Gaussian elimination is the factorization of A as the product LU of a lower triangular matrix L with ones on its diagonal and an upper triangular matrix U, the diagonal entries of which  ... 
doi:10.1016/0024-3795(94)00192-8 fatcat:q2z5d7zznnhyrlvshutqfcfkpa

Fast algorithms for placing large entries along the diagonal of a sparse matrix

Vamsi Kundeti, Sanguthevar Rajasekaran
2010 Journal of Computational and Applied Mathematics  
The equations/rows in the matrix A are often rearranged/permuted before factorization and applying direct or iterative methods to obtain the solution.  ...  Permuting the rows of the matrix A so that the entries with large absolute values lie on the diagonal has several advantages like better numerical stability for direct methods (e.g., Gaussian elimination  ...  dominant matrix.  ... 
doi:10.1016/j.cam.2010.07.002 fatcat:h6w2ba25izhz3csrsymdffgqf4

Combinatorial Problems in Solving Linear Systems [chapter]

Iain Duff, Bora Uçar
2012 Combinatorial Scientific Computing  
On the direct methods side, we discuss issues such as matrix ordering; bipartite matching and matrix scaling for better pivoting; task assignment and scheduling for parallel multifrontal solvers.  ...  On the iterative method side, we discuss preconditioning techniques including incomplete factorization preconditioners, support graph preconditioners, and algebraic multigrid.  ...  Amestoy and Jean-Yves L'Excellent for their contribution to the presented material. We also thankÜmit V. Ç atalyürek for his comments on an earlier version of the paper.  ... 
doi:10.1201/b11644-3 fatcat:wdq7hb343jawxjaqsxz5nihtfq

On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix

I. S. Duff, J. Koster
2001 SIAM Journal on Matrix Analysis and Applications  
Numerical experiments show the e ect of the reorderings and the scaling on the solution of sparse equations by a direct method and by an iterative technique.  ...  The e ect on preconditioning for iterative methods is also discussed.  ...  Acknowledgments 25 We are grateful to Michele Benzi of Los Alamos National Laboratory and Miroslav T uma of the Czech Academy of Sciences for their assistance on the preconditioned iterative methods and  ... 
doi:10.1137/s0895479899358443 fatcat:zxkgkiqc2zde5dik2obllqarrq

An Adaptive Multigrid Method Based on Path Cover [article]

Xiaozhe Hu, Junyuan Lin, Ludmil T. Zikatanov
2018 arXiv   pre-print
The aggregations are then formed by matching along the paths in the path cover. In such manner, we are able to build a multilevel structure at a low computational cost.  ...  The proposed PC-αAMG provides a mechanism to efficiently re-build the multilevel hierarchy during the iterations and leads to a fast nonlinear multilevel algorithm.  ...  In this manner, we can eliminate the dominating smooth errors which cause slow convergence one by one, until desired accuracy is met.  ... 
arXiv:1806.07028v1 fatcat:udsg2sumsjh7td5t3jvlxar6li

Communication complexity as a lower bound for learning in games

Vincent Conitzer, Tuomas Sandholm
2004 Twenty-first international conference on Machine learning - ICML '04  
We characterize exactly the communication complexity of various solution concepts from game theory, namely Nash equilibrium, iterated dominant strategies (both strict and weak), and backwards induction  ...  A fast-growing body of research in the AI and machine learning communities addresses learning in games, where there are multiple learners with different interests.  ...  Acknowledgements This material is based upon work supported by the National Science Foundation under CAREER Award IRI-9703122, Grant IIS-9800994, ITR IIS-0081246, and ITR IIS-0121678.  ... 
doi:10.1145/1015330.1015351 dblp:conf/icml/ConitzerS04 fatcat:ab5yhvf7f5h6bgb3vaekrkzmry

Parallel Sparse PLUQ Factorization modulo p

Charles Bouillaguet, Claire Delaplace, Marie-Emilie Voge
2017 Proceedings of the International Workshop on Parallel Symbolic Computation - PASCO 2017  
Our approach consists in identifying as many pivots as possible before performing any arithmetic operation, based solely on the location of non-zero entries in the input matrix.  ...  Lastly, we describe a multi-thread implementation using OpenMP achieving 70% parallel efficiency on 24 cores on the largest benchmark.  ...  The point is that there is a one-to-one correspondance between alternating paths of A w.r.t M starting by a row vertex and in which all vertices are matched on the one hand, and (directed) paths of G M  ... 
doi:10.1145/3115936.3115944 dblp:conf/issac/BouillaguetDV17 fatcat:mv624ggofvcwxgfms5dus52jmm

MIP-Mitigated Sparse Channel Estimation Using Orthogonal Matching Pursuit Algorithm

Guan Gui, Aihua Kuang, Ling Wang, Aihua Zhang
2013 Research Journal of Applied Sciences Engineering and Technology  
Sparse Multi-Path Channel (SMPC) estimation using Orthogonal Matching Pursuit (OMP) algorithm has took advantage of simplification and fast implementation.  ...  Due to the broadband signal transmission, dominant channel taps are often separated in large delay spread and thus are exhibited highly sparse distribution.  ...  Using OMP, the convergence problem in MP algorithm based on reselection of the atoms is eliminated.  ... 
doi:10.19026/rjaset.5.5102 fatcat:bpvkd3hiknbgbanlilwutrsx2y

Multilevel ILU With Reorderings for Diagonal Dominance

Yousef Saad
2005 SIAM Journal on Scientific Computing  
This paper presents a preconditioning method based on combining two-sided permutations with a multilevel approach.  ...  The nonsymmetric permutation exploits a greedy strategy to put large entries of the matrix in the diagonal of the upper leading submatrix.  ...  I am grateful to Matthias Bollhöfer for numerous insightful discussions on the topic of this paper.  ... 
doi:10.1137/030602733 fatcat:3dv2j457offfjjmgzooefoesge

Who Can Win a Single-Elimination Tournament?

Michael P. Kim, Warut Suksompong, Virginia Vassilevska Williams
2017 SIAM Journal on Discrete Mathematics  
We prove new sufficient conditions on the pairwise match outcome information and the favorite player, under which there is guaranteed to be a seeding where the player wins the tournament.  ...  A single-elimination (SE) tournament is a popular way to select a winner in both sports competitions and in elections.  ...  There is a natural interpretation of iterative matrix solutions as the number of paths of length k starting from each player. Any player in an iterative matrix solution belongs to the uncovered set.  ... 
doi:10.1137/16m1061783 fatcat:gair4cg7rjczxfo5irq37u6s5q

A Survey on Longest Common Subsequence

Deena Nath
2018 International Journal for Research in Applied Science and Engineering Technology  
since space and time complexity rely on it.  ...  Sequence matching is an approach to find a common subsequence among two or more sequences. The subsequence with the largest length is the LCS.  ...  The time and space complexity of this algorithm is O(mn) and O(m) respectively [2] . 3) Dominant matches was another approach given by Hirschberg in 1977.  ... 
doi:10.22214/ijraset.2018.4746 fatcat:b4e2dygazrccpaahekz6caczuq

The simplex method is strongly polynomial for deterministic Markov decision processes [article]

Ian Post, Yinyu Ye
2013 arXiv   pre-print
For a deterministic MDP with n states and m actions, we prove the simplex method runs in O(n^3m^2log^2 n) iterations if the discount factor is uniform and O(n^5m^3log^2 n) iterations if each action has  ...  We identify a set of layers in which the values of primal variables must lie and show that the simplex method always makes progress optimizing one layer, and when the upper layer is updated the algorithm  ...  Each action can be eliminated from cycles and paths, so after 2m such rounds of O(n log n) new cycles the algorithm has converged.  ... 
arXiv:1208.5083v2 fatcat:qrvqltlxxbdg7jl63vw2sbkt6q

The Simplex Method is Strongly Polynomial for Deterministic Markov Decision Processes

Ian Post, Yinyu Ye
2015 Mathematics of Operations Research  
For a deterministic MDP with n states and m actions, we prove the simplex method runs in O(n 3 m 2 log 2 n) iterations if the discount factor is uniform and O(n 5 m 3 log 2 n) iterations if each action  ...  We identify a set of layers in which the values of primal variables must lie and show that the simplex method always makes progress optimizing one layer, and when the upper layer is updated the algorithm  ...  Each action can be eliminated from cycles and paths, so after 2m such rounds of O(n log n) new cycles the algorithm has converged.  ... 
doi:10.1287/moor.2014.0699 fatcat:oerirap3nfbwrorlark5b3hcl4

The simplex method is strongly polynomial for deterministic Markov decision processes [chapter]

Ian Post, Yinyu Ye
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
For a deterministic MDP with n states and m actions, we prove the simplex method runs in O(n 3 m 2 log 2 n) iterations if the discount factor is uniform and O(n 5 m 3 log 2 n) iterations if each action  ...  We identify a set of layers in which the values of primal variables must lie and show that the simplex method always makes progress optimizing one layer, and when the upper layer is updated the algorithm  ...  Each action can be eliminated from cycles and paths, so after 2m such rounds of O(n log n) new cycles the algorithm has converged.  ... 
doi:10.1137/1.9781611973105.105 dblp:conf/soda/PostY13 fatcat:7zn2v5my5jhvrl3ufnekvsuauy
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