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

2010
*
arXiv
*
pre-print

We however establish connections to a

arXiv:1001.0529v1
fatcat:xw4z2geyqjca3kv4hqzsw4evd4
*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. ...##
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A new pivoting strategy for Gaussian elimination

1996
*
Linear Algebra and its Applications
*

This paper discusses a method for determining a good pivoting sequence for Gaussian

doi:10.1016/0024-3795(94)00192-8
fatcat:q2z5d7zznnhyrlvshutqfcfkpa
*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 ...##
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Fast algorithms for placing large entries along the diagonal of a sparse matrix

2010
*
Journal of Computational and Applied Mathematics
*

The equations/rows in the

doi:10.1016/j.cam.2010.07.002
fatcat:h6w2ba25izhz3csrsymdffgqf4
*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*. ...##
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Combinatorial Problems in Solving Linear Systems
[chapter]

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. ...

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

2001
*
SIAM Journal on Matrix Analysis and Applications
*

Numerical experiments show the e ect of the reorderings

doi:10.1137/s0895479899358443
fatcat:zxkgkiqc2zde5dik2obllqarrq
*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*...##
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An Adaptive Multigrid Method Based on Path Cover
[article]

2018
*
arXiv
*
pre-print

The aggregations are then formed by

arXiv:1806.07028v1
fatcat:udsg2sumsjh7td5t3jvlxar6li
*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. ...##
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Communication complexity as a lower bound for learning in games

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,

doi:10.1145/1015330.1015351
dblp:conf/icml/ConitzerS04
fatcat:ab5yhvf7f5h6bgb3vaekrkzmry
*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. ...##
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Parallel Sparse PLUQ Factorization modulo p

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

doi:10.1145/3115936.3115944
dblp:conf/issac/BouillaguetDV17
fatcat:mv624ggofvcwxgfms5dus52jmm
*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 ...##
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MIP-Mitigated Sparse Channel Estimation Using Orthogonal Matching Pursuit Algorithm

2013
*
Research Journal of Applied Sciences Engineering and Technology
*

Sparse Multi-

doi:10.19026/rjaset.5.5102
fatcat:bpvkd3hiknbgbanlilwutrsx2y
*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*. ...##
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Multilevel ILU With Reorderings for Diagonal Dominance

2005
*
SIAM Journal on Scientific Computing
*

This paper presents a preconditioning method based

doi:10.1137/030602733
fatcat:3dv2j457offfjjmgzooefoesge
*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. ...##
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Who Can Win a Single-Elimination Tournament?

2017
*
SIAM Journal on Discrete Mathematics
*

We prove new sufficient conditions

doi:10.1137/16m1061783
fatcat:gair4cg7rjczxfo5irq37u6s5q
*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. ...##
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A Survey on Longest Common Subsequence

2018
*
International Journal for Research in Applied Science and Engineering Technology
*

since space

doi:10.22214/ijraset.2018.4746
fatcat:b4e2dygazrccpaahekz6caczuq
*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. ...##
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The simplex method is strongly polynomial for deterministic Markov decision processes
[article]

2013
*
arXiv
*
pre-print

For a deterministic MDP with n states

arXiv:1208.5083v2
fatcat:qrvqltlxxbdg7jl63vw2sbkt6q
*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. ...##
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The Simplex Method is Strongly Polynomial for Deterministic Markov Decision Processes

2015
*
Mathematics of Operations Research
*

For a deterministic MDP with n states

doi:10.1287/moor.2014.0699
fatcat:oerirap3nfbwrorlark5b3hcl4
*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. ...##
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The simplex method is strongly polynomial for deterministic Markov decision processes
[chapter]

2013
*
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
*

For a deterministic MDP with n states

doi:10.1137/1.9781611973105.105
dblp:conf/soda/PostY13
fatcat:7zn2v5my5jhvrl3ufnekvsuauy
*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. ...
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