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The Parallel Complexity of Positive Linear Programming

1998
*
Parallel Processing Letters
*

In this paper we study

doi:10.1142/s0129626498000511
fatcat:nqf7gy7dfngbdjauquv3h5jpwm
*the**parallel**complexity**of**Positive**Linear**Programming*(PLP), i.e.*the*special case*of**Linear**Programming*in packing/covering form where*the*input constraint matrix and constraint ... Trevisan used*positive**linear**programming*in combination with Luby and Nisan's algorithm to obtain an NC (3=4? )-approximate algorithm for Max SAT. ...*The**parallel**complexity**of*this problem is, by now, well understood. ...##
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Positive Linear Programming Extensions: Parallel Complexity and Applications
[chapter]

2000
*
Lecture Notes in Computer Science
*

In this paper, we propose a general class

doi:10.1007/3-540-44520-x_60
fatcat:tdjex3xi7rhrfmh2qhsjngjaem
*of**linear**programs*that admit efficient*parallel*approximations and use it for efficient*parallel*approximations to hard combinatorial optimization problems. ...*The*largest, in several aspects, general class*of**linear**programs*that admits efficient*parallel*approximation schemes is*the*class*of**positive**linear**programs*(PLP). ... These are, to our knowledge,*the*best known*parallel*approximation results for*the*corresponding problems. Fig. 1 . 1*The**Positive**Linear**Programming*(PLP) model. ...##
###
Page 4630 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

*the*three methods and construction

*of*new

*parallel*algorithms for

*linear*

*programming*.” 93h:90064 90C05 65K05 65Y20 Zhao, G. ...

*of*equality constraints in

*the*orignal

*linear*

*program*. ...

##
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Linear programming and operator means

1989
*
Advances in Applied Mathematics
*

We show by

doi:10.1016/0196-8858(89)90027-4
fatcat:eiac5o2twfhv5b3dp72jghxiau
*linear**programming*techniques that if K has this property, and X"", = sup{ Xl C + K 0 X 2 0}, then ( Xmaxc, c) = inf tr( AY), subject to:*of*two*positive*{ " )y:, = 1 2 0 In*the*case*of**the*...*The*supremnm is taken with respect to*the*partial order generated by*the**positive*semidefinite matrices. In all*of**the*above examples*the*matrix K has exactly one negative eigenvalue. ... A : B*the**parallel*sum*of*two*positive*operator A (see Anderson and Trapp [8] ): 2. ...##
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A canonical form for generalized linear constraints

1992
*
Journal of symbolic computation
*

Important issues encountered include negative constraints,

doi:10.1016/0747-7171(92)90002-l
fatcat:y4zg5lc4xzeb7cqjus75b4bf5u
*the*elimination*of*redundancy and*parallelism*. ...*The*integration*of**the*constraint solving paradigm in*programming*languages raises a number*of*new issues. Foremost is*the*need for a useful canonical form for*the*representation*of*constraints . ... There is a polynomial time algorithm to compute*the*core*of*a*linear**program*. We would like to thank Ilan Adler, Tien Huynh, Michael Maher and Carol Tretkofï for many helpful discussions . ...##
###
Solving Linear and Bilinear Problems with Interval Uncertainty

2015
*
Procedia Engineering
*

Two kinds

doi:10.1016/j.proeng.2015.12.089
fatcat:kwsp3nzxdjbjnebjj7h7a3id6a
*of*optimization problems, which can be used in production planning, have been considered: interval*linear**programming*(ILP), finding equilibrium*position*interval for*the*Von Neumann model (bilinear ...*The*paper presents definitions*of*different solution types and methods for finding these solutions. ...*of*productivity (*the*Frobenius number * ) and stable equilibrium*position*for von Neumann's model lies in solving*the*following bilinear*programming*problem x , w*of*equilibrium*position*w x, , are ...##
###
Page 678 of Mathematical Reviews Vol. , Issue 99a
[page]

1991
*
Mathematical Reviews
*

For this reason it is possible to extend

*the*path through*the*feasible region from*the**positive*real axis to*the*left*complex*half plane. ... We demonstrate that such a paradigm can also yield*parallel*approximation algorithms by showing how to convert certain*linear**programming*relaxations into essentially equiva- lent*positive**linear**programming*...##
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Parallel approximation to high multiplicity scheduling problemsVIAsmooth multi-valued quadratic programming

2007
*
RAIRO - Theoretical Informatics and Applications
*

To deal with

doi:10.1051/ita:2007032
fatcat:tgd4nvqbnfc7zn66ej7wqgpqou
*the**parallel*approximablity*of*these problems, we show first a*parallel*additive approximation procedure to a subclass*of*Multi-valued Quadratic*Programming*, called Smooth Multi-valued QP, ...*The*definition*of*Smooth Multi-valued QP as well as*the*procedure for approximating it in*parallel*are*of*interest independently*of**the*application to*the*scheduling problems considered in this paper. ... Fatos thanks Ray Greenlaw for an early discussion on*the**parallel**complexity**of*quadratic*programming*problems. ...##
###
Implementation and evaluation of MPI-based parallel MD program

2001
*
International Journal of Quantum Chemistry
*

*The*performances

*of*

*the*

*parallel*simulation

*program*implemented with

*the*proposed library are competitive with a custom-designed simulation code. ...

*The*main purpose

*of*this article is to test

*the*PPI library on well-known methods, e.g.,

*the*

*parallel*molecular dynamics (MD) simulation

*of*

*the*monoatomic system by

*the*second-order leapfrog Verlet algorithm ... ACKNOWLEDGMENTS This research was funded under grants J1-106-513, P1-0104-503, J1-0104-7346, and S41-104-001 from

*the*Ministry

*of*Science and Technology

*of*

*the*Republic

*of*Slovenia. ...

##
###
A Canonical Representation of Data-Linear Visualization Algorithms
[article]

2014
*
arXiv
*
pre-print

We have implemented this model in a visualization framework built around

arXiv:1412.4246v1
fatcat:mxj6e76jw5csthlfslciybb4g4
*the*concept*of**linear*-state dataflows. ... We introduce*linear*-state dataflows, a canonical model for a large set*of*visualization algorithms that we call data-*linear*visualizations. ... Sander contributed through major comments on*the*model. I thank*the*rest*of**the*Discovery team: R. Dupuy, S. Haas and*the*technical writers. Also, some Discovery users: C. Lepape, P. Deransart, L. ...##
###
Page 2917 of Mathematical Reviews Vol. , Issue 99d
[page]

1991
*
Mathematical Reviews
*

*Linear*matrix inequalities and

*positive*semidefinite

*programming*(Japanese) (Kyoto, 1996). Stirikaisekikenkytisho Kékyiroku No. 1004 (1997), 1-23. ... We present convergence results for this class

*of*generalized

*parallel*multisplitting relax- ation methods under

*the*condition that

*the*system matrix is an H-matrix with

*positive*diagonal elements.” 99d ...

##
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Independence of negative constraints
[chapter]

1989
*
Lecture Notes in Computer Science
*

This property has in fact a natural interpretation in

doi:10.1007/3-540-50939-9_122
fatcat:pyvl5ej5hvahhgein5pnjbjfjm
*the*context*of**linear**programming*that we exploit here to address problems*of*canonical representations*of**positive*and negative*linear*arithmetic ...*The*independence*of*negative constraints is a recurring phenomenon in logic*programming*. ... Moreover, in terms*of**the*PRAM model*of**parallel*computation,*the*processor*complexity**of**the*algorithm is bounded by*the*number*of*constraints and its time*complexity*by*the*sequential*complexity**of**linear*...##
###
Complexity of Representation and Inference in Compositional Models with Part Sharing
[article]

2013
*
arXiv
*
pre-print

We analyze

arXiv:1301.3560v1
fatcat:cx44gbedingundkhf4s3x5tedq
*the**complexity**of*this model in terms*of*computation time (for serial computers) and numbers*of*nodes (e.g., "neurons") for*parallel*computers. ... In particular, we compute*the**complexity*gains by part sharing and its dependence on how*the*dictionary scales with*the*level*of**the*hierarchy. ... Acknowledgments Many*of**the*ideas in this paper were obtained by analyzing models developed by L. Zhu and Y. Chen in collaboration with*the*first author. G. ...##
###
A parallel-computing solution for optimization of polynomials

2010
*
Proceedings of the 2010 American Control Conference
*

In particular, we design and implement a massively

doi:10.1109/acc.2010.5530905
fatcat:gf4ziplutzec5b4sijs3v4mbam
*parallel*algorithm in MPI which tests*positivity**of*polynomials. ... Unfortunately,*the*high computational costs*of*current algorithms such as sum-*of*-squares has limited its use to relatively small problems. ... If we are to address*the*optimization*of*polynomials in a massively*parallel*world,*the*first thing to consider is*the*problems*of**linear**programming*and semidefinite*programming*. ...##
###
On computational complexity of construction of c -optimal linear regression models over finite experimental domains

2012
*
Tatra Mountains Mathematical Publications
*

and

doi:10.2478/v10127-012-0002-3
fatcat:3jcxi2gzfbbozgxnncspghr2zq
*linear**programming*. ... Assuming some*complexity*-theoretic conjectures, we show that*the*approximate version*of*c-optimality does not have an efficient*parallel*implementation. ... It is a*complexity*-theoretic hardness result showing that*the*problem AOD is at least as hard as general*linear**programming*, or that general*linear**programming*can be seen as a sub-problem*of*AOD. ...
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