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Las Vegas algorithms for linear and integer programming when the dimension is small

Kenneth L. Clarkson
1995 Journal of the ACM  
This paper gives an algcmthm for solving linear programming problems.  ...  The expectations are with respect to the random choices made by the algorithms, and the bounds hold for any gwen input. The techmque can be extended to other convex programming problems.  ...  In Section 3, a time bound is given and proven. The integer programming algorithm is described and analyzed in Section 4. The last section contains some concluding remarks. 2. Linear Programming 2.1.  ... 
doi:10.1145/201019.201036 fatcat:x5r2dzestjay7hwmu27te7jaou

Page 517 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
Karin Gatermann (Berlin) 2001a:68116 68W40 Bein, Wolfgang W. (1-NVLV-C; Las Vegas, NV); Larmore, Lawrence L. (1-NVLV-C; Las Vegas, NV) Trackless online algorithms for the server problem.  ...  The vector scheduling problem is to schedule n d- dimensional tasks on m machines so that the maximum load over all dimensions and all machines is minimized.  ... 

Page 4000 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
A)~' using Moore-Penrose g-inverse and matrix factorization.” 97f:90041 90C05 90C10 Clarkson, Kenneth L. (1-BELL; Murray Hill, NJ) Las Vegas algorithms for linear and integer programming when the dimension  ...  The constant factors do not depend on d. Also, an algorithm is given for integer linear programming.  ... 

Randomization in Graph Optimization Problems: A Survey [chapter]

David R. Karger
2001 Handbook of Randomized Computing  
On the other hand, there is no universal method for making a Monte Carlo algorithm into a Las Vegas one, and indeed some of the algorithms we present are Monte Carlo with no Las Vegas version apparent.  ...  As we are unaware of any algorithm for verifying that a cut is minimum, we have been unable to devise a Las Vegas version of the algorithm.  ...  Target Following Methods for Linear Programming (B. Jansen, C. Roos, and T.  ... 
doi:10.1007/978-1-4615-0013-1_4 fatcat:cmncmhkagrgrhpmf6be3nztgwq

An approximation scheme for strip packing of rectangles with bounded dimensions

W.Fernandez de La Vega, V. Zissimopoulos
1998 Discrete Applied Mathematics  
It is shown that for any positive E the strip-packing problem, i.e. the problem of packing a given list of rectangles into a strip of width 1 and minimum height. can be solled within I c 2: times the optimal  ...  height, in linear time, if the heights and widths of these rectangles are all bounded below by an absolute constant 2 >O.  ...  Acknowledgements WC thank the anonymous referee for several valuable suggestions  ... 
doi:10.1016/s0166-218x(97)00130-3 fatcat:3fwqaemx6radreenkpmctto7ta

Improved algorithms for computing determinants and resultants

Ioannis Z. Emiris, Victor Y. Pan
2005 Journal of Complexity  
We reduce the known bit operation complexity bounds by almost an order of magnitude, in terms of the resultant matrix dimension.  ...  This acceleration is dramatic in a critical application, namely solving polynomial systems and related studies, via computing the resultant.  ...  to use algorithms that require the derivative values, we may represent the Las Vegas algorithm of Theorem 5.3 by a straight-line program (SLP), i.e., without branching.  ... 
doi:10.1016/j.jco.2004.03.003 fatcat:tvpx7r3gf5hphfisdjuvilkwua

Improved algorithms for computing determinants and resultants

I EMIRIS
2004 Journal of Complexity  
We reduce the known bit operation complexity bounds by almost an order of magnitude, in terms of the resultant matrix dimension.  ...  This acceleration is dramatic in a critical application, namely solving polynomial systems and related studies, via computing the resultant.  ...  to use algorithms that require the derivative values, we may represent the Las Vegas algorithm of Theorem 5.3 by a straight-line program (SLP), i.e., without branching.  ... 
doi:10.1016/s0885-064x(04)00022-6 fatcat:xx4udloznnbixe7k6bmlslk2zu

A Robust APTAS for the Classical Bin Packing Problem [chapter]

Leah Epstein, Asaf Levin
2006 Lecture Notes in Computer Science  
Bin packing is a well studied problem which has many applications. In this paper we design a robust APTAS for the problem.  ...  It maintains an approximate solution throughout this process, by slightly adjusting the solution for each new item.  ...  We review the adaptation of the algorithm of Fernandez de la Vega and Lueker [3] , as it appears in [17] , in Section 2.  ... 
doi:10.1007/11786986_20 fatcat:jqhimatg7ngojfemey5pmumnf4

A new method for solving the elliptic curve discrete logarithm problem [article]

Ansari Abdullah, Ayan Mahalanobis, Vivek M. Mallick
2021 arXiv   pre-print
This paper will present necessary algorithms for this attack. We have written a code to verify the conjecture of initial minors using Schur complements.  ...  We were able to solve the problem for groups of order up to 2^50.  ...  The program is developed in such a way that it reads input from an input file and a SageMath [9] script generates the required input files. 6.1. The Las Vegas algorithm with Schur complements.  ... 
arXiv:2005.05039v3 fatcat:jochbk52nrfjtltlvw24gg5enu

Splitting full matrix algebras over algebraic number fields

Gábor Ivanyos, Lajos Rónyai, Josef Schicho
2012 Journal of Algebra  
An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.  ...  A slight modification of the algorithm of Theorem 1 will provide a reasonably small zero divisor: at Step 5 we stop if y is a zero divisor.  ...  Acknowledgments The authors are indebted to an anonymous referee for helpful remarks and suggestions. We are grateful to Géza Kós and Sándor Z. Kiss for discussions on the subject.  ... 
doi:10.1016/j.jalgebra.2012.01.008 fatcat:64qpgfxhojawrhlz2edvgpjdki

A new method for solving the elliptic curve discrete logarithm problem

Ansari Abdullah, Ayan Mahalanobis, Vivek M. Mallick
2021 journal of Groups, complexity, cryptology  
This paper will present necessary algorithms for this attack. We have written a code to verify the conjecture of initial minors using Schur complements.  ...  We were able to solve the problem for groups of order up to $2^{50}$.  ...  The Las Vegas algorithm (Algorithm 1, and also see our earlier work [6] ) that we developed reduces ECDLP to a linear algebra problem.  ... 
doi:10.46298/jgcc.2020.12.2.6649 fatcat:g2sfpb6bpnerdcmbkbpmcocgqa

Splitting full matrix algebras over algebraic number fields [article]

Gábor Ivanyos, Lajos Rónyai, Josef Schicho
2011 arXiv   pre-print
(An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.)  ...  Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n.  ...  We are grateful to Géza Kós and Sándor Z. Kiss for discussions on the subject. We thank Jacques-Arthur Weil for calling our attention to [18] .  ... 
arXiv:1106.6191v3 fatcat:26bvullqyraabpadolzg4emcp4

A fast Las Vegas algorithm for computing the Smith normal form of a polynomial matrix

Arne Storjohann, George Labahn
1997 Linear Algebra and its Applications  
A Las Vegas probabilistic algorithm is presented that finds the Smith normal form S E Q[xl"lX" of a nonsingular input matrix A E Z[ ~1"~".  ...  Applications of the Smith normal form include, for example, solving systems of Diophantine equations over the domain of entries [4], integer programming [S], determining the canonical decomposition of  ...  The algorithm is probabilistic in the Las Vegas sense-an incorrect result will never be returned, but with small probability the algorithm may fail and require repetition.  ... 
doi:10.1016/0024-3795(95)00743-1 fatcat:wdokrgiujzhxfptz7gearxu6ge

The Cover Number of a Matrix and its Algorithmic Applications

Noga Alon, Troy Lee, Adi Shraibman, Marc Herbstritt
2014 International Workshop on Approximation Algorithms for Combinatorial Optimization  
We show bounds on this cover number in terms of VC dimension and the γ 2 norm and give algorithms for enumerating elements of a cover.  ...  This leads to algorithms for computing approximate Nash equilibria that unify and extend several previous results in the literature.  ...  Noga Alon is supported in part by an ERC Advanced grant, a USA-Israeli BSF grant, an ISF grant, the Israeli I-Core program, and by the Simonyi Fund.  ... 
doi:10.4230/lipics.approx-random.2014.34 dblp:conf/approx/AlonLS14 fatcat:nzvswv4g25ambl3skaj5c5gafi

Fuzzy optimal portfolio selection based on multi-objective Mean-Variance-Skewness model by using NSGA-II algorithm

Sharareh Ashrafzadeh, Mehdi Moradzadehfard, Fereydoun Ohadi
2016 Bulletin de la Société royale des sciences de Liège  
Vector evaluated genetic algorithm (VEGA) and non-dominated sorting genetic algorithm (NSGA) were used to compare and evaluate the performance of the proposed solving method.  ...  Constructing an optimal portfolio is a critical decision for investors.  ...  optimization problem in the primary studies, the exact methods such as linear programming, nonlinear programming, and goal programming have been used.  ... 
doi:10.25518/0037-9565.5884 fatcat:7wjrgcs4ofandambsfzthzb27i
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