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### The Parallel Complexity of Positive Linear Programming

Luca Trevisan, Fatos Xhafa
1998 Parallel Processing Letters
In this paper we study 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.  ...

### Positive Linear Programming Extensions: Parallel Complexity and Applications [chapter]

Pavlos S. Efraimidis, Paul G. Spirakis
2000 Lecture Notes in Computer Science
In this paper, we propose a general class 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.  ...

### Linear programming and operator means

T.D Morley
We show by 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.  ...

### A canonical form for generalized linear constraints

Jean-Louis Lassez, Ken McAloon
1992 Journal of symbolic computation
Important issues encountered include negative constraints, 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

A.T. Latipova
2015 Procedia Engineering
Two kinds 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  ...

### Parallel approximation to high multiplicity scheduling problemsVIAsmooth multi-valued quadratic programming

Maria Serna, Fatos Xhafa
2007 RAIRO - Theoretical Informatics and Applications
To deal with 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

R. Trobec, M. ?terk, M. Praprotnik, D. Jane?i?
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]

Thomas Baudel
2014 arXiv   pre-print
We have implemented this model in a visualization framework built around 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  ...

### Independence of negative constraints [chapter]

J. L. Lassez, K. McAloon
1989 Lecture Notes in Computer Science
This property has in fact a natural interpretation in 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]

Alan L. Yuille, Roozbeh Mottaghi
2013 arXiv   pre-print
We analyze 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

Matthew M Peet, Yulia V Peet
2010 Proceedings of the 2010 American Control Conference
In particular, we design and implement a massively 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

Jaromír Antoch, Michal Černý, Milan Hladík
2012 Tatra Mountains Mathematical Publications
and 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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