# Parallel approximation to high multiplicity scheduling problems $VIA$ smooth multi-valued quadratic programming

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2008)

- Volume: 42, Issue: 2, page 237-252
- ISSN: 0988-3754

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topSerna, Maria, and Xhafa, Fatos. "Parallel approximation to high multiplicity scheduling problems $VIA$ smooth multi-valued quadratic programming." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 42.2 (2008): 237-252. <http://eudml.org/doc/245498>.

@article{Serna2008,

abstract = {We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the unweighted model with variable processing requirements and the weighted model with identical processing requirements. These two problems are known to be modelled by a class of quadratic programs that are efficiently solvable in polynomial time. On the parallel setting, both problems are P-complete and hence cannot be efficiently solved in parallel unless P = NC. 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, which is defined by imposing certain restrictions on the coefficients of the instance. We use this procedure to obtain parallel approximation to dense instances of the two problems by observing that dense instances of these problems are instances of smooth multi-valued QP. The dense instances of the problems considered here are defined similarly as for other combinatorial problems in the literature. For such instances we can find in parallel a near optimal schedule. 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.},

author = {Serna, Maria, Xhafa, Fatos},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {parallel approximation; quadratic programming; multiplicity scheduling problem},

language = {eng},

number = {2},

pages = {237-252},

publisher = {EDP-Sciences},

title = {Parallel approximation to high multiplicity scheduling problems $VIA$ smooth multi-valued quadratic programming},

url = {http://eudml.org/doc/245498},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Serna, Maria

AU - Xhafa, Fatos

TI - Parallel approximation to high multiplicity scheduling problems $VIA$ smooth multi-valued quadratic programming

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2008

PB - EDP-Sciences

VL - 42

IS - 2

SP - 237

EP - 252

AB - We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the unweighted model with variable processing requirements and the weighted model with identical processing requirements. These two problems are known to be modelled by a class of quadratic programs that are efficiently solvable in polynomial time. On the parallel setting, both problems are P-complete and hence cannot be efficiently solved in parallel unless P = NC. 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, which is defined by imposing certain restrictions on the coefficients of the instance. We use this procedure to obtain parallel approximation to dense instances of the two problems by observing that dense instances of these problems are instances of smooth multi-valued QP. The dense instances of the problems considered here are defined similarly as for other combinatorial problems in the literature. For such instances we can find in parallel a near optimal schedule. 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.

LA - eng

KW - parallel approximation; quadratic programming; multiplicity scheduling problem

UR - http://eudml.org/doc/245498

ER -

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