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

1995
*
Journal of the ACM
*

This paper gives an algcmthm

doi:10.1145/201019.201036
fatcat:x5r2dzestjay7hwmu27te7jaou
*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. ...##
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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. ...##
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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]

2001
*
Handbook of Randomized Computing
*

On

doi:10.1007/978-1-4615-0013-1_4
fatcat:cmncmhkagrgrhpmf6be3nztgwq
*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. ...##
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An approximation scheme for strip packing of rectangles with bounded dimensions

1998
*
Discrete Applied Mathematics
*

It

doi:10.1016/s0166-218x(97)00130-3
fatcat:3fwqaemx6radreenkpmctto7ta
*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 ...##
###
Improved algorithms for computing determinants and resultants

2005
*
Journal of Complexity
*

We reduce

doi:10.1016/j.jco.2004.03.003
fatcat:tvpx7r3gf5hphfisdjuvilkwua
*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. ...##
###
Improved algorithms for computing determinants and resultants

2004
*
Journal of Complexity
*

We reduce

doi:10.1016/s0885-064x(04)00022-6
fatcat:xx4udloznnbixe7k6bmlslk2zu
*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. ...##
###
A Robust APTAS for the Classical Bin Packing Problem
[chapter]

2006
*
Lecture Notes in Computer Science
*

Bin packing

doi:10.1007/11786986_20
fatcat:jqhimatg7ngojfemey5pmumnf4
*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. ...##
###
A new method for solving the elliptic curve discrete logarithm problem
[article]

2021
*
arXiv
*
pre-print

This paper will present necessary

arXiv:2005.05039v3
fatcat:jochbk52nrfjtltlvw24gg5enu
*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. ...##
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Splitting full matrix algebras over algebraic number fields

2012
*
Journal of Algebra
*

An ff-

doi:10.1016/j.jalgebra.2012.01.008
fatcat:64qpgfxhojawrhlz2edvgpjdki
*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. ...##
###
A new method for solving the elliptic curve discrete logarithm problem

2021
*
journal of Groups, complexity, cryptology
*

This paper will present necessary

doi:10.46298/jgcc.2020.12.2.6649
fatcat:g2sfpb6bpnerdcmbkbpmcocgqa
*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. ...##
###
Splitting full matrix algebras over algebraic number fields
[article]

2011
*
arXiv
*
pre-print

(An ff-

arXiv:1106.6191v3
fatcat:26bvullqyraabpadolzg4emcp4
*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] . ...##
###
A fast Las Vegas algorithm for computing the Smith normal form of a polynomial matrix

1997
*
Linear Algebra and its Applications
*

A

doi:10.1016/0024-3795(95)00743-1
fatcat:wdokrgiujzhxfptz7gearxu6ge
*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. ...##
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The Cover Number of a Matrix and its Algorithmic Applications

2014
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

We show bounds on this cover number in terms of VC

doi:10.4230/lipics.approx-random.2014.34
dblp:conf/approx/AlonLS14
fatcat:nzvswv4g25ambl3skaj5c5gafi
*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. ...##
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Fuzzy optimal portfolio selection based on multi-objective Mean-Variance-Skewness model by using NSGA-II algorithm

2016
*
Bulletin de la Société royale des sciences de Liège
*

Vector evaluated genetic

doi:10.25518/0037-9565.5884
fatcat:7wjrgcs4ofandambsfzthzb27i
*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. ...
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